# 1000 (number)

__: none__

**Short description**__: Natural number__

**Short description**
| ||||
---|---|---|---|---|

Cardinal | one thousand | |||

Ordinal | 1000th (one thousandth) | |||

Factorization | 2^{3} × 5^{3} | |||

Divisors | 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000 | |||

Greek numeral | ,Α´ | |||

Roman numeral | M | |||

Roman numeral (unicode) | M, m, ↀ | |||

Unicode symbol(s) | ↀ | |||

Greek prefix | chilia | |||

Latin prefix | milli | |||

Binary | 1111101000_{2} | |||

Ternary | 1101001_{3} | |||

Quaternary | 33220_{4} | |||

Quinary | 13000_{5} | |||

Senary | 4344_{6} | |||

Octal | 1750_{8} | |||

Duodecimal | 6B4_{12} | |||

Hexadecimal | 3E8_{16} | |||

Vigesimal | 2A0_{20} | |||

Base 36 | RS_{36} | |||

Tamil | ௲ | |||

Chinese | 千 | |||

Punjabi | ੧੦੦੦ |

**1000** or **one thousand** is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: **1,000**.

A group of one thousand things is sometimes known, from Ancient Greek, as a **chiliad**.^{[1]} A period of one thousand years may be known as a chiliad or, more often from Latin, as a millennium. The number 1000 is also sometimes described as a **short thousand** in medieval contexts where it is necessary to distinguish the Germanic concept of 1200 as a long thousand.

## Notation

- The decimal representation for one thousand is
**1000**—a one followed by three zeros, in the general notation;**1 × 10**—in engineering notation, which for this number coincides with:^{3}**1 × 10**exactly—in scientific normalized exponential notation;^{3}**1 E+3**exactly—in scientific E notation.

- The SI prefix for a thousand units is "kilo-", abbreviated to "k"—for instance, a kilogram or "kg" is a thousand grams. This is sometimes extended to non-SI contexts, such as "ka" (kiloannum) being used as a shorthand for periods of 1000 years. In computer science, however, "kilo-" is used more loosely to mean 2 to the 10th power (1024).
- In the SI writing style, a non-breaking space can be used as a thousands separator, i.e., to separate the digits of a number at every power of 1000.
- Multiples of thousands are occasionally represented by replacing their last three zeros with the letter "K" or "k": for instance, writing "$30k" for $30 000 or denoting the Y2K computer bug of the year 2000.
- A thousand units of currency, especially dollars or pounds, are colloquially called a
*grand*. In the United States, this is sometimes abbreviated with a "G" suffix.

## Properties

There are 168 prime numbers less than 1000.^{[2]}

1000 is the 10th icositetragonal number, or 24-gonal number.^{[3]}

1000 has a reduced totient value of 100, and totient of 400. It is equal to the sum of Euler's totient function over the first 57 integers, with 11 integers having a totient value of 1000.

1000 is the smallest number that generates three primes in the fastest way possible by concatenation of decremented numbers: (1,000,999), (1,000,999,998,997), and (1,000,999,998,997,996,995,994,993) are all prime.^{[4]}

The 1000th prime number is 7919. It is a difference of **1** from the order of the smallest sporadic group: [math]\displaystyle{ |\mathrm {M}_{11}| }[/math] = 7920.

## Selected numbers in the range 1001–1999

### 1001 to 1099

**1001**= sphenic number (7 × 11 × 13), pentagonal number, pentatope number**1002**= sphenic number, Mertens function zero, abundant number, number of partitions of 22**1003**= the product of some prime*p*and the*p*^{th}prime, namely*p*= 17.**1004**= heptanacci number^{[5]}**1005**= Mertens function zero, decagonal pyramidal number^{[6]}**1006**= semiprime, product of two distinct isolated primes (2 and 503); unusual number; square-free number; number of compositions (ordered partitions) of 22 into squares; sum of two distinct pentatope numbers (5 and 1001); number of undirected Hamiltonian paths in 4 by 5 square grid graph;^{[7]}record gap between twin primes;^{[8]}number that is the sum of 7 positive 5th powers.^{[9]}In decimal: equidigital number; when turned around, the number looks like a prime, 9001; its cube can be concatenated from other cubes, 1_0_1_8_1_0_8_216 ("_" indicates concatenation, 0 = 0^{3}, 1 = 1^{3}, 8 = 2^{3}, 216 = 6^{3})^{[10]}**1007**= number that is the sum of 8 positive 5th powers^{[11]}**1008**= divisible by the number of primes below it**1009**= smallest four-digit prime, palindromic in bases 11, 15, 19, 24 and 28: (838_{11}, 474_{15}, 2F2_{19}, 1I1_{24}, 181_{28}). It is also a Lucky prime and Chen prime.**1010**= 10^{3}+ 10,^{[12]}Mertens function zero**1011**= the largest*n*such that 2^{n}contains 101 and doesn't contain 11011, Harshad number in bases 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75 (and 202 other bases), number of partitions of 1 into reciprocals of positive integers <= 16 Egyptian fraction^{[13]}**1012**= ternary number, (32_{10}) quadruple triangular number (triangular number is 253),^{[14]}number of partitions of 1 into reciprocals of positive integers <= 17 Egyptian fraction^{[13]}**1013**= Sophie Germain prime,^{[15]}centered square number,^{[16]}Mertens function zero**1014**= 2^{10}-10,^{[17]}Mertens function zero, sum of the nontriangular numbers between successive triangular numbers**1015**= square pyramidal number^{[18]}**1016**= member of the Mian–Chowla sequence,^{[19]}stella octangula number, number of surface points on a cube with edge-length 14^{[20]}**1017**= generalized triacontagonal number^{[21]}**1018**= Mertens function zero, 1018^{16}+ 1 is prime^{[22]}**1019**= Sophie Germain prime,^{[15]}safe prime,^{[23]}Chen prime**1020**= polydivisible number**1021**= twin prime with**1019**. It is also a Lucky prime.**1022**= Friedman number**1023**= sum of five consecutive primes (193 + 197 + 199 + 211 + 223);^{[24]}the number of three-dimensional polycubes with 7 cells;^{[25]}number of elements in a 9-simplex; highest number one can count to on one's fingers using binary; magic number used in Global Positioning System signals.**1024**= 32^{2}= 4^{5}= 2^{10}, the number of bytes in a kilobyte (in 1999, the IEC coined kibibyte to use for 1024 with kilobyte being 1000, but this convention has not been widely adopted). 1024 is the smallest 4-digit square and also a Friedman number.**1025**= Proth number 2^{10}+ 1; member of Moser–de Bruijn sequence, because its base-4 representation (100001_{4}) contains only digits 0 and 1, or it's a sum of distinct powers of 4 (4^{5}+ 4^{0}); Jacobsthal-Lucas number; hypotenuse of primitive Pythagorean triangle**1026**= sum of two distinct powers of 2 (1024 + 2)**1027**= sum of the squares of the first eight primes; can be written from base 2 to base 18 using only the digits 0 to 9.**1028**= sum of totient function for first 58 integers; can be written from base 2 to base 18 using only the digits 0 to 9; number of primes <= 2^{13}.^{[26]}**1029**= can be written from base 2 to base 18 using only the digits 0 to 9.**1030**= generalized heptagonal number**1031**= exponent and number of ones for the fifth base-10 repunit prime,^{[27]}Sophie Germain prime,^{[15]}super-prime, Chen prime**1032**= sum of two distinct powers of 2 (1024 + 8)**1033**= emirp, twin prime with**1031****1034**= sum of 12 positive 9th powers^{[28]}**1035**= triangular number,^{[29]}hexagonal number^{[30]}**1036**= central polygonal number^{[31]}**1037**= number in E-toothpick sequence^{[32]}**1038**= even integer that is an unordered sum of two primes in exactly*n*ways^{[33]}**1039**= prime of the form 8n+7,^{[34]}number of partitions of 30 that do not contain 1 as a part,^{[35]}Chen prime**1040**= 4^{5}+ 4^{2}: sum of distinct powers of 4.^{[36]}The number of pieces that could be seen in a 6 × 6 × 6× 6 Rubik's Tesseract.**1041**= sum of 11 positive 5th powers^{[37]}**1042**= sum of 12 positive 5th powers^{[38]}**1043**= number whose sum of even digits and sum of odd digits are even^{[39]}**1044**= sum of distinct powers of 4^{[36]}**1045**= octagonal number^{[40]}**1046**= coefficient of f(q) (3rd order mock theta function)^{[41]}**1047**= number of ways to split a strict composition of*n*into contiguous subsequences that have the same sum^{[42]}**1048**= number of partitions of*n*into squarefree parts^{[43]}**1049**= Sophie Germain prime,^{[15]}highly cototient number,^{[44]}Chen prime**1050**= 1050_{8}to decimal becomes a pronic number (552_{10}),^{[45]}number of parts in all partitions of 29 into distinct parts^{[46]}**1051**= centered pentagonal number,^{[47]}centered decagonal number**1052**= number that is the sum of 9 positive 6th powers^{[48]}**1053**= triangular matchstick number^{[49]}**1054**= centered triangular number^{[50]}**1055**= number that is the sum of 12 positive 6th powers^{[51]}**1056**= pronic number^{[52]}**1057**= central polygonal number^{[53]}**1058**= number that is the sum of 4 positive 5th powers,^{[54]}area of a square with diagonal 46^{[55]}**1059**= number*n*such that n^{4}is written in the form of a sum of four positive 4th powers^{[56]}**1060**= sum of the first 25 primes**1061**= emirp, twin prime with**1063****1062**= number that is not the sum of two palindromes^{[57]}**1063**= super-prime, sum of seven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167); near-wall-sun-sun prime^{[58]}**1064**= sum of two positive cubes^{[59]}**1065**= generalized duodecagonal^{[60]}**1066**= number whose sum of their divisors is a square^{[61]}**1067**= number of strict integer partitions of*n*in which are empty or have smallest part not dividing the other ones^{[62]}**1068**= number that is the sum of 7 positive 5th powers,^{[9]}total number of parts in all partitions of 15^{[63]}**1069**= emirp^{[64]}**1070**= number that is the sum of 9 positive 5th powers^{[65]}**1071**= heptagonal number^{[66]}**1072**= centered heptagonal number^{[67]}**1073**= number that is the sum of 12 positive 5th powers^{[38]}**1074**= number that is not the sum of two palindromes^{[57]}**1075**= number non-sum of two palindromes^{[57]}**1076**= number of strict trees weight*n*^{[68]}**1077**= number where 7 outnumbers every other digit in the number^{[69]}**1078**= Euler transform of negative integers^{[70]}**1079**= every positive integer is the sum of at most 1079 tenth powers.**1080**= pentagonal number^{[71]}**1081**= triangular number,^{[29]}member of Padovan sequence^{[72]}**1082**= central polygonal number^{[31]}**1083**= three-quarter square,^{[73]}number of partitions of 53 into prime parts**1084**= third spoke of a hexagonal spiral,^{[74]}1084^{64}+ 1 is prime**1085**= number of partitions of*n*into distinct parts > or = 2^{[75]}**1086**= Smith number,^{[76]}sum of totient function for first 59 integers**1087**= super-prime, cousin prime, lucky prime^{[77]}**1088**= octo-triangular number, (triangular number result being 136)^{[78]}sum of two distinct powers of 2, (1024 + 64)^{[79]}number that is divisible by exactly seven primes with the inclusion of multiplicity^{[80]}**1089**= 33^{2}, nonagonal number, centered octagonal number, first natural number whose digits in its decimal representation get reversed when multiplied by 9.^{[81]}**1090**= sum of 5 positive 5th powers^{[82]}**1091**= cousin prime and twin prime with**1093****1092**= divisible by the number of primes below it**1093**= the smallest Wieferich prime (the only other known Wieferich prime is 3511^{[83]}), twin prime with**1091**and star number^{[84]}**1094**= sum of 9 positive 5th powers,^{[65]}1094^{64}+ 1 is prime**1095**= sum of 10 positive 5th powers,^{[85]}number that is not the sum of two palindromes**1096**= hendecagonal number,^{[86]}number of strict solid partitions of 18^{[87]}**1097**= emirp,^{[64]}Chen prime**1098**= multiple of 9 containing digit 9 in its base-10 representation^{[88]}**1099**= number where 9 outnumbers every other digit^{[89]}

### 1100 to 1199

**1100**= number of partitions of 61 into distinct squarefree parts^{[90]}**1101**= pinwheel number^{[91]}**1102**= sum of totient function for first 60 integers**1103**= Sophie Germain prime,^{[15]}balanced prime^{[92]}**1104**= Keith number^{[93]}**1105**= 33^{2}+ 4^{2}= 32^{2}+ 9^{2}= 31^{2}+ 12^{2}= 23^{2}+ 24^{2}, Carmichael number,^{[94]}magic constant of*n*×*n*normal magic square and*n*-queens problem for*n*= 13, decagonal number,^{[95]}centered square number,^{[16]}Fermat pseudoprime^{[96]}**1106**= number of regions into which the plane is divided when drawing 24 ellipses^{[97]}**1107**= number of non-isomorphic strict T_{0}multiset partitions of weight 8^{[98]}**1108**= number k such that k^{64}+ 1 is prime**1109**= Friedlander-Iwaniec prime,^{[99]}Chen prime**1110**= k such that 2^{k}+ 3 is prime^{[100]}**1111**= 11 × 101, palindrome that is a product of two palindromic primes^{[101]}**1112**= k such that 9^{k}- 2 is a prime^{[102]}**1113**= number of strict partions of 40^{[103]}**1114**= number of ways to write 22 as an orderless product of orderless sums^{[104]}**1115**= number of partitions of 27 into a prime number of parts^{[105]}**1116**= divisible by the number of primes below it**1117**= number of diagonally symmetric polyominoes with 16 cells,^{[106]}Chen prime**1118**= number of unimodular 2 × 2 matrices having all terms in {0,1,...,21}^{[107]}**1119**= number of bipartite graphs with 9 nodes^{[108]}**1120**= number k such that k^{64}+ 1 is prime**1121**= number of squares between 34^{2}and 34^{4}.^{[109]}**1122**= pronic number,^{[52]}divisible by the number of primes below it**1123**= balanced prime^{[92]}**1124**= Leyland number^{[110]}**1125**= Achilles number**1126**= number of 2 × 2 non-singular integer matrices with entries from {0, 1, 2, 3, 4, 5}^{[111]}**1127**= maximal number of pieces that can be obtained by cutting an annulus with 46 cuts^{[112]}**1128**= triangular number,^{[29]}hexagonal number,^{[30]}divisible by the number of primes below it**1129**= number of lattice points inside a circle of radius 19^{[113]}**1130**= skiponacci number^{[114]}**1131**= number of edges in the hexagonal triangle T(26)^{[115]}**1132**= number of simple unlabeled graphs with 9 nodes of 2 colors whose components are complete graphs^{[116]}**1133**= number of primitive subsequences of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}^{[117]}**1134**= divisible by the number of primes below it, triangular matchstick number^{[49]}**1135**= centered triangular number^{[118]}**1136**= number of independent vertex sets and vertex covers in the 7-sunlet graph^{[119]}**1137**= sum of values of vertices at level 5 of the hyperbolic Pascal pyramid^{[120]}**1138**= recurring number in the works of George Lucas and his companies, beginning with his first feature film –*THX 1138*; particularly, a special code for Easter eggs on*Star Wars*DVDs.**1139**= wiener index of the windmill graph D(3,17)^{[121]}**1140**= tetrahedral number^{[122]}**1141**= 7-Knödel number^{[123]}**1142**= n such that n^{32}+ 1 is prime^{[124]}**1143**= number of set partitions of 8 elements with 2 connectors^{[125]}**1144**is not the sum of a pair of twin primes^{[126]}**1145**= 5-Knödel number^{[127]}**1146**is not the sum of a pair of twin primes^{[126]}**1147**= 31 × 37 (a product of 2 successive primes)^{[128]}**1148**is not the sum of a pair of twin primes^{[126]}**1149**= a product of two palindromic primes^{[129]}**1150**= number of 11-iamonds without bilateral symmetry.^{[130]}**1151**= first prime following a prime gap of 22,^{[131]}Chen prime**1152**= highly totient number,^{[132]}3-smooth number (2^{7}×3^{2}), area of a square with diagonal 48,^{[55]}Achilles number**1153**= super-prime, Proth prime^{[133]}**1154**= 2 × 24^{2}+ 2 = number of points on surface of tetrahedron with edgelength 24^{[134]}**1155**= number of edges in the join of two cycle graphs, both of order 33^{[135]}**1156**= 34^{2}, octahedral number,^{[136]}centered pentagonal number,^{[47]}centered hendecagonal number.^{[137]}**1157**= smallest number that can be written as n^2+1 without any prime factors that can be written as a^2+1.^{[138]}**1158**= number of points on surface of octahedron with edgelength 17^{[139]}**1159**= member of the Mian–Chowla sequence,^{[19]}a centered octahedral number^{[140]}**1160**= octagonal number^{[141]}**1161**= sum of the first 26 primes**1162**= pentagonal number,^{[71]}sum of totient function for first 61 integers**1163**= smallest prime > 34^{2}.^{[142]}See Legendre's conjecture. Chen prime.**1165**= 5-Knödel number^{[127]}**1166**= heptagonal pyramidal number^{[143]}**1167**= number of rational numbers which can be constructed from the set of integers between 1 and 43^{[144]}**1169**= highly cototient number^{[44]}**1170**= highest possible score in a National Academic Quiz Tournaments (NAQT) match**1171**= super-prime**1172**= number of subsets of first 14 integers that have a sum divisible by 14^{[145]}**1173**= number of simple triangulation on a plane with 9 nodes^{[146]}**1174**= number of widely totally strongly normal compositions of 16**1175**= maximal number of pieces that can be obtained by cutting an annulus with 47 cuts^{[112]}**1176**= triangular number^{[29]}**1177**= heptagonal number^{[66]}**1178**= number of surface points on a cube with edge-length 15^{[20]}**1179**= number of different permanents of binary 7*7 matrices^{[147]}**1180**= smallest number of non-integral partitions into non-integral power >1000.^{[148]}**1181**= smallest k over 1000 such that 8*10^k-49 is prime.^{[149]}**1182**= number of necklaces possible with 14 beads of 2 colors (that cannot be turned over)^{[150]}**1183**= pentagonal pyramidal number**1184**= amicable number with 1210^{[151]}**1185**= number of partitions of 45 into pairwise relatively prime parts^{[152]}**1186**= number of diagonally symmetric polyominoes with 15 cells,^{[106]}number of partitions of 54 into prime parts**1187**= safe prime,^{[23]}Stern prime,^{[153]}balanced prime,^{[92]}Chen prime**1188**= first 4 digit multiple of 18 to contain 18^{[154]}**1189**= number of squares between 35^{2}and 35^{4}.^{[109]}**1190**= pronic number,^{[52]}number of cards to build an 28-tier house of cards^{[155]}**1191**= 35^{2}- 35 + 1 = H_{35}(the 35th Hogben number)^{[156]}**1192**= sum of totient function for first 62 integers**1193**= a number such that 4^{1193}- 3^{1193}is prime, Chen prime**1194**=number of permutations that can be reached with 8 moves of 2 bishops and 1 rook on a 3 × 3 chessboard^{[157]}**1195**= smallest four digit number for which a^{-1}(n) is an integer is a(n) is 2*a(n-1) - (-1)^{n}^{[158]}**1196**= [math]\displaystyle{ \sum_{k=1}^{38} \sigma(k) }[/math]^{[159]}**1197**= pinwheel number^{[91]}**1198**= centered heptagonal number^{[67]}**1199**= area of the 20th conjoined trapezoid^{[160]}

### 1200 to 1299

**1200**= the**long thousand**, ten "long hundreds" of 120 each, the traditional reckoning of large numbers in Germanic languages, the number of households the Nielsen ratings sample,^{[161]}number k such that k^{64}+ 1 is prime**1201**= centered square number,^{[16]}super-prime, centered decagonal number**1202**= number of regions the plane is divided into by 25 ellipses^{[97]}**1203**: first 4 digit number in the coordinating sequence for the (2,6,∞) tiling of the hyperbolic plane^{[162]}**1204**: magic constant of a 7 × 7 × 7 magic cube^{[163]}**1205**= number of partitions of 28 such that the number of odd parts is a part^{[164]}**1206**= 29-gonal number^{[165]}**1207**= composite de Polignac number^{[166]}**1209**= The product of all ordered non-empty subsets of {3,1} if {a,b} is a||b: 1209=1*3*13*31**1210**= amicable number with 1184^{[167]}**1211**= composite de Polignac number^{[166]}**1213**= emirp**1214**= sum of first 39 composite numbers^{[168]}**1215**= number of edges in the hexagonal triangle T(27)^{[115]}**1216**= nonagonal number^{[169]}**1217**= super-prime, Proth prime^{[133]}**1218**= triangular matchstick number^{[49]}**1219**= Mertens function zero, centered triangular number^{[118]}**1220**= Mertens function zero, number of binary vectors of length 16 containing no singletons^{[170]}**1221**= product of the first two digit, and three digit repdigit**1222**= hexagonal pyramidal number**1223**= Sophie Germain prime,^{[15]}balanced prime, 200th prime number^{[92]}**1224**= number of edges in the join of two cycle graphs, both of order 34^{[135]}**1225**= 35^{2}, square triangular number,^{[171]}hexagonal number,^{[30]}centered octagonal number^{[172]}**1226**= number of rooted identity trees with 15 nodes^{[173]}**1227**= smallest number representable as the sum of 3 triangular numbers in 27 ways^{[174]}**1228**= sum of totient function for first 63 integers**1229**= Sophie Germain prime,^{[15]}number of primes between 0 and 10000, emirp**1230**= the Mahonian number: T(9, 6)^{[175]}**1231**= smallest mountain emirp, as 121, smallest mountain number is 11 × 11**1232**= number of labeled ordered set of partitions of a 7-set into odd parts^{[176]}**1233**= 12^{2}+ 33^{2}**1234**= number of parts in all partitions of 30 into distinct parts,^{[46]}smallest whole number containing all numbers from 1 to 4**1235**= excluding duplicates, contains the first four Fibbonacci numbers^{[177]}**1236**= 617 + 619: sum of twin prime pair^{[178]}**1237**= prime of the form 2p-1**1238**= number of partitions of 31 that do not contain 1 as a part^{[35]}**1239**= toothpick number in 3D^{[179]}**1240**= square pyramidal number^{[18]}**1241**= centered cube number^{[180]}**1242**= decagonal number^{[95]}**1243**= composite de Polignac number^{[166]}**1244**= number of complete partitions of 25^{[181]}**1245**= Number of labeled spanning intersecting set-systems on 5 vertices.^{[182]}**1246**= number of partitions of 38 such that no part occurs more than once^{[183]}**1247**= pentagonal number^{[71]}**1248**= the first four powers of 2 concatenated together**1249**= emirp, trimorphic number^{[184]}**1250**= area of a square with diagonal 50^{[55]}**1251**= 2 × 25^{2}+ 1 = number of different 2 × 2 determinants with integer entries from 0 to 25^{[185]}**1252**= 2 × 25^{2}+ 2 = number of points on surface of tetrahedron with edgelength 25^{[134]}**1253**= number of partitions of 23 with at least one distinct part^{[186]}**1254**= number of partitions of 23 into relatively prime parts^{[187]}**1255**= Mertens function zero, number of ways to write 23 as an orderless product of orderless sums,^{[104]}number of partitions of 23^{[188]}**1256**= Mertens function zero**1257**= number of lattice points inside a circle of radius 20^{[113]}**1258**= Mertens function zero**1259**= highly cototient number^{[44]}**1260**= highly composite number,^{[189]}pronic number,^{[52]}the smallest vampire number,^{[190]}sum of totient function for first 64 integers, number of strict partions of 41^{[103]}and appears twice in the Book of Revelation**1261**= star number,^{[84]}Mertens function zero**1262**= maximal number of regions the plane is divided into by drawing 36 circles^{[191]}**1263**= rounded total surface area of a regular tetrahedron with edge length 27^{[192]}**1264**= sum of the first 27 primes**1265**= number of rooted trees with 43 vertices in which vertices at the same level have the same degree^{[193]}**1266**= centered pentagonal number,^{[47]}Mertens function zero**1267**= 7-Knödel number^{[123]}**1268**= number of partitions of 37 into prime power parts^{[194]}**1269**= least number of triangles of the Spiral of Theodorus to complete 11 revolutions^{[195]}**1270**= 25 + 24×26 + 23×27,^{[196]}Mertens function zero**1271**= sum of first 40 composite numbers^{[168]}**1272**= sum of first 41 nonprimes^{[197]}**1273**= 19 × 67 = 19 × prime(19)^{[198]}**1274**= sum of the nontriangular numbers between successive triangular numbers**1275**= triangular number,^{[29]}sum of the first 50 natural numbers**1276**= number of irredundant sets in the 25-cocktail party graph^{[199]}**1277**= the start of a prime constellation of length 9 (a "prime nonuple")**1278**= number of Narayana's cows and calves after 20 years^{[200]}**1279**= Mertens function zero, Mersenne prime exponent**1280**= Mertens function zero, number of parts in all compositions of 9^{[201]}**1281**= octagonal number^{[141]}**1282**= Mertens function zero, number of partitions of 46 into pairwise relatively prime parts^{[152]}**1283**= safe prime^{[23]}**1284**= 641 + 643: sum of twin prime pair^{[178]}**1285**= Mertens function zero, number of free nonominoes, number of parallelogram polyominoes with 10 cells.^{[202]}**1286**= number of inequivalent connected planar figures that can be formed from five 1 X 2 rectangles (or dominoes) such that each pair of touching rectangles shares exactly one edge, of length 1, and the adjacency graph of the rectangles is a tree^{[203]}**1287**= [math]\displaystyle{ {13 \choose 5} }[/math]^{[204]}**1288**= heptagonal number^{[66]}**1289**= Sophie Germain prime,^{[15]}Mertens function zero**1291**= Mertens function zero**1292**= Mertens function zero**1294**= rounded volume of a regular octahedron with edge length 14^{[205]}**1295**= number of edges in the join of two cycle graphs, both of order 35^{[135]}**1296**= 36^{2}= 6^{4}, sum of the cubes of the first eight positive integers, the number of rectangles on a normal 8 × 8 chessboard, also the maximum font size allowed in Adobe InDesign**1297**= super-prime, Mertens function zero, pinwheel number^{[91]}**1298**= number of partitions of 55 into prime parts**1299**= Mertens function zero, number of partitions of 52 such that the smallest part is greater than or equal to number of parts^{[206]}

### 1300 to 1399

**1300**= Sum of the first 4 fifth powers, mertens function zero, largest possible win margin in an NAQT match**1301**= centered square number,^{[16]}Honaker prime,^{[207]}number of trees with 13 unlabeled nodes^{[208]}**1302**= Mertens function zero, number of edges in the hexagonal triangle T(28)^{[115]}**1303**= prime of form 21n+1 and 31n+1^{[209]}^{[210]}**1304**= sum of 1304_{6}and 1304_{9}which is 328+976**1305**= triangular matchstick number^{[49]}**1306**= Mertens function zero. In base 10, raising the digits of 1306 to powers of successive integers equals itself: 1306 = 1^{1}+ 3^{2}+ 0^{3}+ 6^{4}. 135, 175, 518, and 598 also have this property. Centered triangular number.^{[118]}**1307**= safe prime^{[23]}**1308**= sum of totient function for first 65 integers**1309**= the first sphenic number followed by two consecutive such number**1310**= smallest number in the middle of a set of three sphenic numbers**1311**= number of integer partitions of 32 with no part dividing all the others^{[211]}**1312**= member of the Mian-Chowla sequence;^{[19]}code for "ACAB" itself an acronym for "all cops are bastards"^{[212]}**1313**= sum of all parts of all partitions of 14^{[213]}**1314**= number of integer partitions of 41 whose distinct parts are connected^{[214]}**1315**= 10^(2n+1)-7*10^n-1 is prime.^{[215]}**1316**= Euler transformation of sigma(11)^{[216]}**1317**= 1317 Only odd four digit number to divide the concatenation of all number up to itself in base 25^{[217]}**1318**= Mertens function zero**1319**= safe prime^{[23]}**1320**= 659 + 661: sum of twin prime pair^{[178]}**1321**= Friedlander-Iwaniec prime^{[99]}**1322**= area of the 21th conjoined trapezoid^{[160]}**1323**= Achilles number**1324**= if D(n) is the nth representation of 1, 2 arranged lexicographically. 1324 is the first non-1 number which is D(D(x))^{[218]}**1325**= Markov number,^{[219]}centered tetrahedral number^{[220]}**1326**= triangular number,^{[29]}hexagonal number,^{[30]}Mertens function zero**1327**= first prime followed by 33 consecutive composite numbers**1328**= sum of totient function for first 66 integers**1329**= Mertens function zero, sum of first 41 composite numbers^{[168]}**1330**= tetrahedral number,^{[110]}forms a Ruth–Aaron pair with 1331 under second definition**1331**= 11^{3}, centered heptagonal number,^{[67]}forms a Ruth–Aaron pair with 1330 under second definition. This is the only non-trivial cube of the form*x*^{2}+*x*− 1, for*x*= 36.**1332**= pronic number^{[52]}**1333**= 37^{2}- 37 + 1 = H_{37}(the 37th Hogben number)^{[156]}**1334**= maximal number of regions the plane is divided into by drawing 37 circles^{[191]}**1335**= pentagonal number,^{[71]}Mertens function zero**1336**= Mertens function zero**1337**= Used in the novel form of spelling called leet. Approximate melting point of gold in kelvins.**1338**= Mertens function zero**1339**= First 4 digit number to appear twice in the sequence of sum of cubes of primes dividing n^{[221]}**1340**= k such that 5 × 2^{k}- 1 is prime^{[222]}**1341**= First mountain number with 2 jumps of more than one.**1342**= [math]\displaystyle{ \sum_{k=1}^{40} \sigma(k) }[/math],^{[159]}Mertens function zero**1343**= cropped hexagone^{[223]}**1344**= 37^{2}- 5^{2}, the only way to express 1344 as a difference of prime squares^{[224]}**1345**= k such that k, k+1 and k+2 are products of two primes^{[225]}**1346**= number of locally disjointed rooted trees with 10 nodes^{[226]}**1347**= concatenation of first 4 Lucas numbers^{[227]}**1348**= number of ways to stack 22 pennies such that every penny is in a stack of one or two^{[228]}**1349**= Stern-Jacobsthal number^{[229]}**1350**= nonagonal number^{[169]}**1351**= number of partitions of 28 into a prime number of parts^{[105]}**1352**= number of surface points on a cube with edge-length 16,^{[20]}Achilles number**1353**= 2 × 26^{2}+ 1 = number of different 2 × 2 determinants with integer entries from 0 to 26^{[185]}**1354**= 2 × 26^{2}+ 2 = number of points on surface of tetrahedron with edgelength 26^{[134]}**1356**is not the sum of a pair of twin primes^{[126]}**1357**= number of nonnegative solutions to x^{2}+ y^{2}≤ 41^{2}^{[230]}**1358**= rounded total surface area of a regular tetrahedron with edge length 28^{[192]}**1360**= 37^{2}- 3^{2}, the only way to express 1360 as a difference of prime squares^{[224]}**1361**= first prime following a prime gap of 34,^{[131]}centered decagonal number, Honaker prime^{[207]}**1362**= number of achiral integer partitions of 48^{[231]}**1365**= pentatope number^{[232]}**1367**= safe prime,^{[23]}balanced prime, sum of three, nine, and eleven consecutive primes (449 + 457 + 461, 131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 + 173, and 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151),^{[92]}**1368**= number of edges in the join of two cycle graphs, both of order 36^{[135]}**1369**= 37^{2}, centered octagonal number^{[172]}**1370**= σ_{2}(37): sum of squares of divisors of 37^{[233]}**1371**= sum of the first 28 primes**1372**= Achilles number**1373**= number of lattice points inside a circle of radius 21^{[113]}**1374**= number of unimodular 2 × 2 matrices having all terms in {0,1,...,23}^{[107]}**1375**= decagonal pyramidal number^{[234]}**1376**= primitive abundant number (abundant number all of whose proper divisors are deficient numbers)^{[235]}**1377**= maximal number of pieces that can be obtained by cutting an annulus with 51 cuts^{[112]}**1378**= triangular number^{[29]}**1379**= magic constant of*n*×*n*normal magic square and*n*-queens problem for*n*= 14.**1380**= number of 8-step mappings with 4 inputs^{[236]}**1381**= centered pentagonal number^{[47]}Mertens function zero**1382**= first 4 digit tetrachi number^{[237]}**1384**= [math]\displaystyle{ \sum_{k=1}^{41} \sigma(k) }[/math]^{[159]}**1385**= up/down number^{[238]}**1386**= octagonal pyramidal number^{[239]}**1387**= 5th Fermat pseudoprime of base 2,^{[240]}22nd centered hexagonal number and the 19th decagonal number,^{[95]}second Super-Poulet number.^{[241]}**1389**= sum of first 42 composite numbers^{[168]}**1391**= number of rational numbers which can be constructed from the set of integers between 1 and 47^{[144]}**1392**= number of edges in the hexagonal triangle T(29)^{[115]}**1393**= 7-Knödel number^{[123]}**1394**= sum of totient function for first 67 integers**1395**= vampire number,^{[190]}member of the Mian–Chowla sequence^{[19]}triangular matchstick number^{[49]}**1396**= centered triangular number^{[118]}**1398**= number of integer partitions of 40 whose distinct parts are connected^{[214]}

### 1400 to 1499

**1400**= number of sum-free subsets of {1, ..., 15}^{[242]}**1401**= pinwheel number^{[91]}**1402**= number of integer partitions of 48 whose augmented differences are distinct^{[243]}**1404**= heptagonal number^{[66]}**1405**= 26^{2}+ 27^{2}, 7^{2}+ 8^{2}+ ... + 16^{2}, centered square number^{[16]}**1406**= pronic number,^{[52]}semi-meandric number^{[244]}**1407**= 38^{2}- 38 + 1 = H_{38}(the 38th Hogben number)^{[156]}**1408**= maximal number of regions the plane is divided into by drawing 38 circles^{[191]}**1409**= super-prime, Sophie Germain prime,^{[15]}smallest number whose eighth power is the sum of 8 eighth powers, Proth prime^{[133]}**1414**= smallest composite that when added to sum of prime factors reaches a prime after 27 iterations^{[245]}**1415**= the Mahonian number: T(8, 8)^{[175]}**1417**= number of partitions of 32 in which the number of parts divides 32^{[246]}**1419**= Zeisel number^{[247]}**1420**= Number of partitions of 56 into prime parts**1423**= 200 + 1223 and the 200th prime is 1223^{[248]}Also Used as a Hate symbol**1424**= number of nonnegative solutions to x^{2}+ y^{2}≤ 42^{2}^{[230]}**1425**= self-descriptive number in base 5**1426**= sum of totient function for first 68 integers, pentagonal number,^{[71]}number of strict partions of 42^{[103]}**1429**= number of partitions of 53 such that the smallest part is greater than or equal to number of parts^{[206]}**1430**= Catalan number^{[249]}**1431**= triangular number,^{[29]}hexagonal number^{[30]}**1432**= member of Padovan sequence^{[72]}**1433**= super-prime, Honaker prime,^{[207]}typical port used for remote connections to Microsoft SQL Server databases**1434**= rounded volume of a regular tetrahedron with edge length 23^{[250]}**1435**= vampire number;^{[190]}the standard railway gauge in millimetres, equivalent to 4 feet 8^{1}⁄_{2}inches (1.435 m)**1437**= smallest number of complexity 20: smallest number requiring 20 1's to build using +, * and ^^{[251]}**1438**= k such that 5 × 2^{k}- 1 is prime^{[222]}**1439**= Sophie Germain prime,^{[15]}safe prime^{[23]}**1440**= a highly totient number^{[132]}and a 481-gonal number. Also, the number of minutes in one day, the blocksize of a standard 3+1/2 floppy disk, and the horizontal resolution of WXGA(II) computer displays**1441**= star number^{[84]}**1442**= number of parts in all partitions of 31 into distinct parts^{[46]}**1443**= the sum of the second trio of three-digit permutable primes in decimal: 337, 373, and 733. Also the number of edges in the join of two cycle graphs, both of order 37^{[135]}**1444**= 38^{2}, smallest pandigital number in Roman numerals**1446**= number of points on surface of octahedron with edgelength 19^{[139]}**1447**= super-prime, happy number**1448**= number k such that phi(prime(k)) is a square^{[252]}**1449**= Stella octangula number**1450**= σ_{2}(34): sum of squares of divisors of 34^{[233]}**1451**= Sophie Germain prime^{[15]}**1452**= first Zagreb index of the complete graph K_{12}^{[253]}**1453**= Sexy prime with 1459**1454**= 3 × 22^{2}+ 2 = number of points on surface of square pyramid of side-length 22^{[254]}**1455**= k such that geometric mean of phi(k) and sigma(k) is an integer^{[255]}**1457**= 2 × 27^{2}− 1 = a twin square^{[256]}**1458**= maximum determinant of an 11 by 11 matrix of zeroes and ones, 3-smooth number (2×3^{6})**1459**= Sexy prime with 1453, sum of nine consecutive primes (139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181), pierpont prime**1460**= Nickname of the original "Doc Marten's" boots, released 1 April 1960**1461**= number of partitions of 38 into prime power parts^{[194]}**1462**= (35 - 1) × (35 + 8) = the first Zagreb index of the wheel graph with 35 vertices^{[257]}**1463**= total number of parts in all partitions of 16^{[63]}**1464**= rounded total surface area of a regular icosahedron with edge length 13^{[258]}**1465**= 5-Knödel number^{[127]}**1469**= octahedral number,^{[136]}highly cototient number^{[44]}**1470**= pentagonal pyramidal number,^{[259]}sum of totient function for first 69 integers**1471**= super-prime, centered heptagonal number^{[67]}**1473**= cropped hexagone^{[223]}**1476**= coreful perfect number^{[260]}**1477**= 7-Knödel number^{[123]}**1479**= number of planar partitions of 12^{[261]}**1480**= sum of the first 29 primes**1481**= Sophie Germain prime^{[15]}**1482**= pronic number,^{[52]}number of unimodal compositions of 15 where the maximal part appears once^{[262]}**1483**= 39^{2}- 39 + 1 = H_{39}(the 39th Hogben number)^{[156]}**1484**= maximal number of regions the plane is divided into by drawing 39 circles^{[191]}**1485**= triangular number**1486**= number of strict solid partitions of 19^{[87]}**1487**= safe prime^{[23]}**1488**= triangular matchstick number^{[49]}Also used as a hate symbol**1489**= centered triangular number^{[118]}**1490**= tetranacci number^{[263]}**1491**= nonagonal number,^{[169]}Mertens function zero**1492**= Mertens function zero**1493**= Stern prime^{[153]}**1494**= sum of totient function for first 70 integers**1496**= square pyramidal number^{[18]}**1497**= skiponacci number^{[114]}**1498**= number of flat partitions of 41^{[264]}**1499**= Sophie Germain prime,^{[15]}super-prime

### 1500 to 1599

**1500**= hypotenuse in three different Pythagorean triangles^{[265]}**1501**= centered pentagonal number^{[47]}**1502**= number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most 47^{[266]}**1503**= least number of triangles of the Spiral of Theodorus to complete 12 revolutions^{[195]}**1504**= primitive abundant number (abundant number all of whose proper divisors are deficient numbers)^{[235]}**1507**= number of partitions of 32 that do not contain 1 as a part^{[35]}**1508**= heptagonal pyramidal number^{[143]}**1509**= pinwheel number^{[91]}**1510**= deficient number, odious number**1511**= Sophie Germain prime,^{[15]}balanced prime^{[92]}**1512**= k such that geometric mean of phi(k) and sigma(k) is an integer^{[255]}**1513**= centered square number^{[16]}**1514**= sum of first 44 composite numbers^{[168]}**1517**= number of lattice points inside a circle of radius 22^{[113]}**1518**= Mertens function zero**1519**= Mertens function zero**1520**= pentagonal number,^{[71]}Mertens function zero, forms a Ruth–Aaron pair with 1521 under second definition**1521**= 39^{2}, Mertens function zero, centered octagonal number,^{[172]}forms a Ruth–Aaron pair with 1520 under second definition**1522**= k such that 5 × 2^{k}- 1 is prime^{[222]}**1523**= super-prime, Mertens function zero, safe prime,^{[23]}member of the Mian–Chowla sequence^{[19]}**1524**= Mertens function zero, k such that geometric mean of phi(k) and sigma(k) is an integer^{[255]}**1525**= heptagonal number,^{[66]}Mertens function zero**1526**= number of conjugacy classes in the alternating group A_{27}^{[267]}**1527**= Mertens function zero**1528**= Mertens function zero, rounded total surface area of a regular octahedron with edge length 21^{[268]}**1529**= composite de Polignac number^{[166]}**1530**= vampire number^{[190]}**1531**= prime number, centered decagonal number, Mertens function zero**1532**= Mertens function zero**1534**= number of achiral integer partitions of 50^{[231]}**1535**= Thabit number**1536**= a common size of microplate, 3-smooth number (2^{9}×3), number of threshold functions of exactly 4 variables^{[269]}**1537**= Keith number,^{[93]}Mertens function zero**1538**= number of surface points on a cube with edge-length 17^{[20]}**1539**= maximal number of pieces that can be obtained by cutting an annulus with 54 cuts^{[112]}**1540**= triangular number, hexagonal number,^{[30]}decagonal number,^{[95]}tetrahedral number^{[110]}**1541**= octagonal number^{[141]}**1543**= Mertens function zero**1544**= Mertens function zero, number of partitions of integer partitions of 17 where all parts have the same length^{[270]}**1546**= Mertens function zero**1547**= hexagonal pyramidal number**1548**= coreful perfect number^{[260]}**1549**= de Polignac prime^{[271]}**1552**= Number of partitions of 57 into prime parts**1556**= sum of the squares of the first nine primes**1557**= number of graphs with 8 nodes and 13 edges^{[272]}**1558**= number k such that k^{64}+ 1 is prime**1559**= Sophie Germain prime^{[15]}**1560**= pronic number^{[52]}**1561**= a centered octahedral number,^{[140]}number of series-reduced trees with 19 nodes^{[273]}**1562**= maximal number of regions the plane is divided into by drawing 40 circles^{[191]}**1564**= sum of totient function for first 71 integers**1565**= [math]\displaystyle{ \sqrt{1036^2+1173^2} }[/math] and [math]\displaystyle{ 1036+1173=47^2 }[/math]^{[274]}**1566**= number k such that k^{64}+ 1 is prime**1567**= number of partitions of 24 with at least one distinct part^{[186]}**1568**= Achilles number^{[275]}**1569**= 2 × 28^{2}+ 1 = number of different 2 × 2 determinants with integer entries from 0 to 28^{[185]}**1570**= 2 × 28^{2}+ 2 = number of points on surface of tetrahedron with edgelength 28^{[134]}**1571**= Honaker prime^{[207]}**1572**= member of the Mian–Chowla sequence^{[19]}**1575**= odd abundant number,^{[276]}sum of the nontriangular numbers between successive triangular numbers, number of partitions of 24^{[188]}**1578**= sum of first 45 composite numbers^{[168]}**1579**= number of partitions of 54 such that the smallest part is greater than or equal to number of parts^{[206]}**1580**= number of achiral integer partitions of 51^{[231]}**1581**= number of edges in the hexagonal triangle T(31)^{[115]}**1583**= Sophie Germain prime**1584**= triangular matchstick number^{[49]}**1585**= Riordan number, centered triangular number^{[118]}**1586**= area of the 23th conjoined trapezoid^{[160]}**1588**= sum of totient function for first 72 integers**1589**= composite de Polignac number^{[166]}**1590**= rounded volume of a regular icosahedron with edge length 9^{[277]}**1591**= rounded volume of a regular octahedron with edge length 15^{[205]}**1593**= sum of the first 30 primes**1594**= minimal cost of maximum height Huffman tree of size 17^{[278]}**1595**= number of non-isomorphic set-systems of weight 10**1596**= triangular number**1597**= Fibonacci prime,^{[279]}Markov prime,^{[219]}super-prime, emirp**1598**= number of unimodular 2 × 2 matrices having all terms in {0,1,...,25}^{[107]}**1599**= number of edges in the join of two cycle graphs, both of order 39^{[135]}

### 1600 to 1699

**1600**= 40^{2}, structured great rhombicosidodecahedral number,^{[280]}repdigit in base 7 (4444_{7}), street number on Pennsylvania Avenue of the White House, length in meters of a common High School Track Event, perfect score on SAT (except from 2005 to 2015)**1601**= Sophie Germain prime, Proth prime,^{[133]}the novel*1601 (Mark Twain)***1602**= number of points on surface of octahedron with edgelength 20^{[139]}**1603**= number of partitions of 27 with nonnegative rank^{[281]}**1606**= enneagonal pyramidal number^{[282]}**1608**= [math]\displaystyle{ \sum_{k=1}^{44} \sigma(k) }[/math]^{[159]}**1609**= cropped hexagonal number^{[223]}**1610**= number of strict partions of 43^{[103]}**1611**= number of rational numbers which can be constructed from the set of integers between 1 and 51^{[144]}**1617**= pentagonal number^{[71]}**1618**= centered heptagonal number^{[67]}**1619**= palindromic prime in binary, safe prime^{[23]}**1620**= 809 + 811: sum of twin prime pair^{[178]}**1621**= super-prime, pinwheel number^{[91]}**1624**= number of squares in the Aztec diamond of order 28^{[283]}**1625**= centered square number^{[16]}**1626**= centered pentagonal number^{[47]}**1629**= rounded volume of a regular tetrahedron with edge length 24^{[250]}**1630**= number k such that k^64 + 1 is prime**1632**= number of acute triangles made from the vertices of a regular 18-polygon^{[284]}**1633**= star number^{[84]}**1634**= Narcissistic number in base 10**1635**= number of partitions of 56 whose reciprocal sum is an integer^{[285]}**1636**= number of nonnegative solutions to x^{2}+ y^{2}≤ 45^{2}^{[230]}**1637**= prime island: least prime whose adjacent primes are exactly 30 apart^{[286]}**1638**= harmonic divisor number,^{[287]}5 × 2^{1638}- 1 is prime^{[222]}**1639**= nonagonal number^{[169]}**1640**= pronic number^{[52]}**1641**= 41^{2}- 41 + 1 = H_{41}(the 41st Hogben number)^{[156]}**1642**= maximal number of regions the plane is divided into by drawing 41 circles^{[191]}**1643**= sum of first 46 composite numbers^{[168]}**1644**= 821 + 823: sum of twin prime pair^{[178]}**1645**= number of 16-celled pseudo still lifes in Conway's Game of Life, up to rotation and reflection^{[288]}**1646**= number of graphs with 8 nodes and 14 edges^{[272]}**1647**and 1648 are both divisible by cubes^{[289]}**1648**= number of partitions of 34^{3}into distinct cubes^{[290]}**1649**= highly cototient number,^{[44]}Leyland number^{[110]}**1650**= number of cards to build an 33-tier house of cards^{[155]}**1651**= heptagonal number^{[66]}**1652**= number of partitions of 29 into a prime number of parts^{[105]}**1653**= triangular number, hexagonal number,^{[30]}number of lattice points inside a circle of radius 23^{[113]}**1654**= number of partitions of 42 into divisors of 42^{[291]}**1655**= rounded volume of a regular dodecahedron with edge length 6^{[292]}**1656**= 827 + 829: sum of twin prime pair^{[178]}**1657**= cuban prime,^{[293]}prime of the form 2p-1**1658**= smallest composite that when added to sum of prime factors reaches a prime after 25 iterations^{[245]}**1659**= number of rational numbers which can be constructed from the set of integers between 1 and 52^{[144]}**1660**= sum of totient function for first 73 integers**1661**= 11 × 151, palindrome that is a product of two palindromic primes^{[101]}**1662**= number of partitions of 49 into pairwise relatively prime parts^{[152]}**1663**= a prime number and 5^{1663}- 4^{1663}is a 1163-digit prime number^{[294]}**1664**= k such that k, k+1 and k+2 are sums of 2 squares^{[295]}**1665**= centered tetrahedral number^{[220]}**1666**= largest efficient pandigital number in Roman numerals (each symbol occurs exactly once)**1667**= 228 + 1439 and the 228th prime is 1439^{[248]}**1668**= number of partitions of 33 into parts all relatively prime to 33^{[296]}**1669**= super-prime, smallest prime with a gap of exactly 24 to the next prime^{[297]}**1670**= number of compositions of 12 such that at least two adjacent parts are equal^{[298]}**1671**divides the sum of the first 1671 composite numbers^{[299]}**1672**= 41^{2}- 2^{2}, the only way to express 1672 as a difference of prime squares^{[224]}**1673**= RMS number^{[300]}**1674**= k such that geometric mean of phi(k) and sigma(k) is an integer^{[255]}**1675**= Kin number^{[301]}**1676**= number of partitions of 34 into parts each of which is used a different number of times^{[302]}**1677**= 41^{2}- 3^{2}, the only way to express 1677 as a difference of prime squares^{[224]}**1678**= n such that n^{32}+ 1 is prime^{[124]}**1679**= highly cototient number,^{[44]}semiprime (23 × 73, see also Arecibo message), number of parts in all partitions of 32 into distinct parts^{[46]}**1680**= highly composite number,^{[189]}number of edges in the join of two cycle graphs, both of order 40^{[135]}**1681**= 41^{2}, smallest number yielded by the formula*n*^{2}+*n*+ 41 that is not a prime; centered octagonal number^{[172]}**1682**= and**1683**is a member of a Ruth–Aaron pair (first definition)**1683**= triangular matchstick number^{[49]}**1684**= centered triangular number^{[118]}**1685**= 5-Knödel number^{[127]}**1686**= [math]\displaystyle{ \sum_{k=1}^{45} \sigma(k) }[/math]^{[159]}**1687**= 7-Knödel number^{[123]}**1688**= number of finite connected sets of positive integers greater than one with least common multiple 72^{[303]}**1689**= [math]\displaystyle{ 9!!\sum_{k=0}^{4} \frac{1}{2k+1} }[/math]^{[304]}**1690**= number of compositions of 14 into powers of 2^{[305]}**1691**= the same upside down, which makes it a strobogrammatic number^{[306]}**1692**= coreful perfect number^{[260]}**1693**= smallest prime > 41^{2}.^{[142]}**1694**= number of unimodular 2 × 2 matrices having all terms in {0,1,...,26}^{[107]}**1695**= magic constant of*n*×*n*normal magic square and*n*-queens problem for*n*= 15. Number of partitions of 58 into prime parts**1696**= sum of totient function for first 74 integers**1697**= Friedlander-Iwaniec prime^{[99]}**1698**= number of rooted trees with 47 vertices in which vertices at the same level have the same degree^{[193]}**1699**= number of rooted trees with 48 vertices in which vertices at the same level have the same degree^{[193]}

### 1700 to 1799

**1700**= σ_{2}(39): sum of squares of divisors of 39^{[233]}**1701**= [math]\displaystyle{ \left\{ {8 \atop 4} \right\} }[/math], decagonal number, hull number of the U.S.S. Enterprise on*Star Trek***1702**= palindromic in 3 consecutive bases: 898_{14}, 787_{15}, 6A6_{16}**1703**= 1703131131 / 1000077 and the divisors of 1703 are 1703, 131, 13 and 1^{[307]}**1704**= sum of the squares of the parts in the partitions of 18 into two distinct parts^{[308]}**1705**= tribonacci number^{[309]}**1706**= 1 + 4 + 16 + 64 + 256 + 1024 + 256 + 64 + 16 + 4 + 1 sum of fifth row of triangle of powers of 4^{[310]}**1707**= number of partitions of 30 in which the number of parts divides 30^{[246]}**1708**= 2^{2}× 7 × 61 a number whose product of prime indices 1 × 1 × 4 × 18 is divisible by its sum of prime factors 2 + 2 + 7 + 61^{[311]}**1709**= first of a sequence of eight primes formed by adding 57 in the middle. 1709, 175709, 17575709, 1757575709, 175757575709, 17575757575709, 1757575757575709 and 175757575757575709 are all prime, but 17575757575757575709 = 232433 × 75616446785773**1710**= maximal number of pieces that can be obtained by cutting an annulus with 57 cuts^{[112]}**1711**= triangular number, centered decagonal number**1712**= number of irredundant sets in the 29-cocktail party graph^{[199]}**1713**= number of aperiodic rooted trees with 12 nodes^{[312]}**1714**= number of regions formed by drawing the line segments connecting any two of the 18 perimeter points of an 3 × 6 grid of squares^{[313]}**1715**= k such that geometric mean of phi(k) and sigma(k) is an integer^{[255]}**1716**= 857 + 859: sum of twin prime pair^{[178]}**1717**= pentagonal number^{[71]}**1718**= [math]\displaystyle{ \sum_{d|12} \binom{12}{d} }[/math]^{[314]}**1719**= composite de Polignac number^{[166]}**1720**= sum of the first 31 primes**1721**= twin prime; number of squares between 42^{2}and 42^{4}.^{[109]}**1722**= Giuga number,^{[315]}pronic number^{[52]}**1723**= super-prime**1724**= maximal number of regions the plane is divided into by drawing 42 circles^{[191]}**1725**= 47^{2}- 22^{2}= (prime(15))^{2}- (nonprime(15))^{2}^{[316]}**1726**= number of partitions of 44 into distinct and relatively prime parts^{[317]}**1727**= area of the 24th conjoined trapezoid^{[160]}**1728**= the quantity expressed as 1000 in duodecimal, that is, the cube of twelve (called a great gross), and so, the number of cubic inches in a cubic foot, palindromic in base 11 (1331_{11}) and 23 (363_{23})**1729**= taxicab number, Carmichael number, Zeisel number, centered cube number, Hardy–Ramanujan number. In the decimal expansion of e the first time all 10 digits appear in sequence starts at the 1729th digit (or 1728th decimal place). In 1979 the rock musical*Hair*closed on Broadway in New York City after 1729 performances. Palindromic in bases 12, 32, 36.**1730**= 3 × 24^{2}+ 2 = number of points on surface of square pyramid of side-length 24^{[254]}**1731**= k such that geometric mean of phi(k) and sigma(k) is an integer^{[255]}**1732**= [math]\displaystyle{ \sum_{k=0}^5 \binom{5}{k}^k }[/math]^{[318]}**1733**= Sophie Germain prime, palindromic in bases 3, 18, 19.**1734**= surface area of a cube of edge length 17^{[319]}**1735**= number of partitions of 55 such that the smallest part is greater than or equal to number of parts^{[206]}**1736**= sum of totient function for first 75 integers, number of surface points on a cube with edge-length 18^{[20]}**1737**= pinwheel number^{[91]}**1738**= number of achiral integer partitions of 52^{[231]}**1739**= number of 1s in all partitions of 30 into odd parts^{[320]}**1740**= number of squares in the Aztec diamond of order 29^{[283]}**1741**= super-prime, centered square number^{[16]}**1742**= number of regions the plane is divided into by 30 ellipses^{[97]}**1743**= wiener index of the windmill graph D(3,21)^{[121]}**1744**= k such that k, k+1 and k+2 are sums of 2 squares^{[295]}**1745**= 5-Knödel number^{[127]}**1746**= number of unit-distance graphs on 8 nodes^{[321]}**1747**= balanced prime^{[92]}**1748**= number of partitions of 55 into distinct parts in which the number of parts divides 55^{[322]}**1749**= number of integer partitions of 33 with no part dividing all the others^{[211]}**1750**= hypotenuse in three different Pythagorean triangles^{[265]}**1751**= cropped hexagone^{[223]}**1752**= 79^{2}- 67^{2}, the only way to express 1752 as a difference of prime squares^{[224]}**1753**= balanced prime^{[92]}**1754**= k such that 5*2^{k}- 1 is prime^{[222]}**1755**= number of integer partitions of 50 whose augmented differences are distinct^{[243]}**1756**= centered pentagonal number^{[47]}**1757**= least number of triangles of the Spiral of Theodorus to complete 13 revolutions^{[195]}**1758**= [math]\displaystyle{ \sum_{k=1}^{46} \sigma(k) }[/math]^{[159]}**1759**= de Polignac prime^{[271]}**1760**= the number of yards in a mile**1761**= k such that k, k+1 and k+2 are products of two primes^{[225]}**1762**= number of binary sequences of length 12 and curling number 2^{[323]}**1763**= number of edges in the join of two cycle graphs, both of order 41^{[135]}**1764**= 42^{2}**1765**= number of stacks, or planar partitions of 15^{[324]}**1766**= number of points on surface of octahedron with edgelength 21^{[139]}**1767**= σ(28^{2}) = σ(35^{2})^{[325]}**1768**= number of nonequivalent dissections of an hendecagon into 8 polygons by nonintersecting diagonals up to rotation^{[326]}**1769**= maximal number of pieces that can be obtained by cutting an annulus with 58 cuts^{[112]}**1770**= triangular number, hexagonal number,^{[30]}Seventeen Seventy, town in Australia**1771**= tetrahedral number^{[110]}**1772**= centered heptagonal number,^{[67]}sum of totient function for first 76 integers**1773**= number of words of length 5 over the alphabet {1,2,3,4,5} such that no two even numbers appear consecutively^{[327]}**1774**= number of rooted identity trees with 15 nodes and 5 leaves^{[328]}**1775**= [math]\displaystyle{ \sum_{1\leq i\leq 10}prime(i)\cdot(2\cdot i-1) }[/math]: sum of piles of first 10 primes^{[329]}**1776**= square star number.^{[330]}The number of pieces that could be seen in a 7 × 7 × 7× 7 Rubik's Tesseract.**1777**= smallest prime > 42^{2}.^{[142]}**1778**= least k >= 1 such that the remainder when 6^{k}is divided by k is 22^{[331]}**1779**= number of achiral integer partitions of 53^{[231]}**1780**= number of lattice paths from (0, 0) to (7, 7) using E (1, 0) and N (0, 1) as steps that horizontally cross the diagonal y = x with even many times^{[332]}**1781**= the first 1781 digits of e form a prime^{[333]}**1782**= heptagonal number^{[66]}**1783**= de Polignac prime^{[271]}**1784**= number of subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} such that every pair of distinct elements has a different quotient^{[334]}**1785**= square pyramidal number,^{[18]}triangular matchstick number^{[49]}**1786**= centered triangular number^{[118]}**1787**= super-prime, sum of eleven consecutive primes (137 + 139 + 149 + 151 + 157 + 163 + 167 + 173 + 179 + 181 + 191)**1788**= Euler transform of -1, -2, ..., -34^{[335]}**1789**= number of wiggly sums adding to 17 (terms alternately increase and decrease or vice versa)^{[336]}**1790**= number of partitions of 50 into pairwise relatively prime parts^{[152]}**1791**= largest natural number that cannot be expressed as a sum of at most four hexagonal numbers.**1792**= Granville number**1793**= number of lattice points inside a circle of radius 24^{[113]}**1794**= nonagonal number,^{[169]}number of partitions of 33 that do not contain 1 as a part^{[35]}**1795**= number of heptagons with perimeter 38^{[337]}**1796**= k such that geometric mean of phi(k) and sigma(k) is an integer^{[255]}**1797**= number k such that phi(prime(k)) is a square^{[252]}**1798**= 2 × 29 × 31 = 10_{2}× 11101_{2}× 11111_{2}, which yield zero when the prime factors are xored together^{[338]}**1799**= 2 × 30^{2}− 1 = a twin square^{[256]}

### 1800 to 1899

**1800**= pentagonal pyramidal number,^{[259]}Achilles number, also, in da Ponte's*Don Giovanni*, the number of women Don Giovanni had slept with so far when confronted by Donna Elvira, according to Leporello's tally**1801**= cuban prime, sum of five and nine consecutive primes (349 + 353 + 359 + 367 + 373 and 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227)^{[293]}**1802**= 2 × 30^{2}+ 2 = number of points on surface of tetrahedron with edgelength 30,^{[134]}number of partitions of 30 such that the number of odd parts is a part^{[164]}**1803**= number of decahexes that tile the plane isohedrally but not by translation or by 180-degree rotation (Conway criterion)^{[339]}**1804**= number k such that k^64 + 1 is prime**1805**= number of squares between 43^{2}and 43^{4}.^{[109]}**1806**= pronic number,^{[52]}product of first four terms of Sylvester's sequence, primary pseudoperfect number,^{[340]}only number for which*n*equals the denominator of the*n*th Bernoulli number,^{[341]}Schröder number^{[342]}**1807**= fifth term of Sylvester's sequence^{[343]}**1808**= maximal number of regions the plane is divided into by drawing 43 circles^{[191]}**1809**= sum of first 17 super-primes^{[344]}**1810**= [math]\displaystyle{ \sum_{k=0}^4 \binom{4}{k}^4 }[/math]^{[345]}**1811**= Sophie Germain prime**1812**= n such that n^{32}+ 1 is prime^{[124]}**1813**= number of polyominoes with 26 cells, symmetric about two orthogonal axes^{[346]}**1814**= 1 + 6 + 36 + 216 + 1296 + 216 + 36 + 6 + 1 = sum of 4th row of triangle of powers of six^{[347]}**1815**= polygonal chain number [math]\displaystyle{ \#(P^3_{2,1}) }[/math]^{[348]}**1816**= number of strict partions of 44^{[103]}**1817**= total number of prime parts in all partitions of 20^{[349]}**1818**= n such that n^{32}+ 1 is prime^{[124]}**1819**= sum of the first 32 primes, minus 32^{[350]}**1820**= pentagonal number,^{[71]}pentatope number,^{[232]}number of compositions of 13 whose run-lengths are either weakly increasing or weakly decreasing^{[351]}**1821**= member of the Mian–Chowla sequence^{[19]}**1822**= number of integer partitions of 43 whose distinct parts are connected^{[214]}**1823**= super-prime, safe prime^{[23]}**1824**= 43^{2}- 5^{2}, the only way to express 1824 as a difference of prime squares^{[224]}**1825**= octagonal number^{[141]}**1826**= decagonal pyramidal number^{[234]}**1827**= vampire number^{[190]}**1828**= meandric number, open meandric number, appears twice in the first 10 decimal digits of*e***1829**= composite de Polignac number^{[166]}**1830**= triangular number**1831**= smallest prime with a gap of exactly 16 to next prime (1847)^{[352]}**1832**= sum of totient function for first 77 integers**1833**= number of atoms in a decahedron with 13 shells^{[353]}**1834**= octahedral number,^{[136]}sum of the cubes of the first five primes**1835**= absolute value of numerator of [math]\displaystyle{ D_6^{(5)} }[/math]^{[354]}**1836**= factor by which a proton is more massive than an electron**1837**= star number^{[84]}**1838**= number of unimodular 2 × 2 matrices having all terms in {0,1,...,27}^{[107]}**1839**= [math]\displaystyle{ \lfloor \sqrt[3]{13!} \rfloor }[/math]^{[355]}**1840**= 43^{2}- 3^{2}, the only way to express 1840 as a difference of prime squares^{[224]}**1841**= Mertens function zero**1842**= number of unlabeled rooted trees with 11 nodes^{[356]}**1843**= Mertens function zero**1844**= Mertens function zero**1845**= Mertens function zero**1846**= sum of first 49 composite numbers^{[168]}**1847**= super-prime**1848**= number of edges in the join of two cycle graphs, both of order 42^{[135]}**1849**= 43^{2}, palindromic in base 6 (= 12321_{6}), centered octagonal number^{[172]}**1850**= Number of partitions of 59 into prime parts**1851**= sum of the first 32 primes**1852**= number of quantales on 5 elements, up to isomorphism^{[357]}**1853**= Mertens function zero**1854**= Mertens function zero**1855**= rencontres number: number of permutations of [7] with exactly one fixed point^{[358]}**1856**= sum of totient function for first 78 integers**1857**= Mertens function zero, pinwheel number^{[91]}**1858**= number of 14-carbon alkanes C_{14}H_{30}ignoring stereoisomers^{[359]}**1859**= composite de Polignac number^{[166]}**1860**= number of squares in the Aztec diamond of order 30^{[360]}**1861**= centered square number,^{[16]}Mertens function zero**1862**= Mertens function zero, forms a Ruth–Aaron pair with 1863 under second definition**1863**= Mertens function zero, forms a Ruth–Aaron pair with 1862 under second definition**1864**= Mertens function zero, [math]\displaystyle{ \frac{1864!-2}{2} }[/math] is a prime^{[361]}**1865**= 12345_{6}: Largest senary metadrome (number with digits in strict ascending order in base 6)^{[362]}**1866**= Mertens function zero, number of plane partitions of 16 with at most two rows^{[363]}**1867**= prime de Polignac number^{[271]}**1868**= smallest number of complexity 21: smallest number requiring 21 1's to build using +, * and ^^{[251]}**1869**= Hultman number: S_{H}(7, 4)^{[364]}**1870**= decagonal number^{[95]}**1871**= the first prime of the 2 consecutive twin prime pairs: (1871, 1873) and (1877, 1879)^{[365]}**1872**= first Zagreb index of the complete graph K_{13}^{[253]}**1873**= number of Narayana's cows and calves after 21 years^{[200]}**1874**= area of the 25th conjoined trapezoid^{[160]}**1875**= 50^{2}- 25^{2}**1876**= number k such that k^64 + 1 is prime**1877**= number of partitions of 39 where 39 divides the product of the parts^{[366]}**1878**= n such that n^{32}+ 1 is prime^{[124]}**1879**= a prime with square index^{[367]}**1880**= the 10th element of the self convolution of Lucas numbers^{[368]}**1881**= tricapped prism number^{[369]}**1882**= number of linearly separable boolean functions in 4 variables^{[370]}**1883**= number of conjugacy classes in the alternating group A_{28}^{[267]}**1884**= k such that 5*2^{k}- 1 is prime^{[222]}**1885**= Zeisel number^{[247]}**1886**= number of partitions of 6^{4}into fourth powers^{[371]}**1887**= number of edges in the hexagonal triangle T(34)^{[115]}**1888**= primitive abundant number (abundant number all of whose proper divisors are deficient numbers)^{[235]}**1889**= Sophie Germain prime, highly cototient number^{[44]}**1890**= triangular matchstick number^{[49]}**1891**= triangular number, hexagonal number,^{[30]}centered pentagonal number,^{[47]}centered triangular number^{[118]}**1892**= pronic number^{[52]}**1893**= 44^{2}- 44 + 1 = H_{44}(the 44th Hogben number)^{[156]}**1894**= maximal number of regions the plane is divided into by drawing 44 circles^{[191]}**1895**= Stern-Jacobsthal number^{[229]}**1896**= member of the Mian-Chowla sequence^{[19]}**1897**= member of Padovan sequence,^{[72]}number of triangle-free graphs on 9 vertices^{[372]}**1898**= smallest multiple of n whose digits sum to 26^{[373]}**1899**= cropped hexagone^{[223]}

### 1900 to 1999

**1900**= number of primes <= 2^{14}.^{[26]}Also*1900*(film) or*Novecento*, 1976 movie. 1900 was the year Thorold Gosset introduced his list of semiregular polytopes; it is also the year Max Brückner published his study of polyhedral models, including stellations of the icosahedron, such as the novel final stellation of the icosahedron.**1901**= Sophie Germain prime, centered decagonal number**1902**= number of symmetric plane partitions of 27^{[374]}**1903**= generalized catalan number^{[375]}**1904**= number of flat partitions of 43^{[264]}**1905**= Fermat pseudoprime^{[96]}**1906**= number n such that 3^{n}- 8 is prime^{[376]}**1907**= safe prime,^{[23]}balanced prime^{[92]}**1908**= coreful perfect number^{[260]}**1909**= hyperperfect number^{[377]}**1910**= number of compositions of 13 having exactly one fixed point^{[378]}**1911**= heptagonal pyramidal number^{[143]}**1912**= size of 6th maximum raising after one blind in pot-limit poker^{[379]}**1913**= super-prime, Honaker prime^{[207]}**1914**= number of bipartite partitions of 12 white objects and 3 black ones^{[380]}**1915**= number of nonisomorphic semigroups of order 5^{[381]}**1916**= sum of first 50 composite numbers^{[168]}**1917**= number of partitions of 51 into pairwise relatively prime parts^{[152]}**1918**= heptagonal number^{[66]}**1919**= smallest number with reciprocal of period length 36 in base 10^{[382]}**1920**= sum of the nontriangular numbers between successive triangular numbers**1921**= 4-dimensional centered cube number^{[383]}**1922**= Area of a square with diagonal 62^{[55]}**1923**= 2 × 31^{2}+ 1 = number of different 2 X 2 determinants with integer entries from 0 to 31^{[185]}**1924**= 2 × 31^{2}+ 2 = number of points on surface of tetrahedron with edgelength 31^{[134]}**1925**= number of ways to write 24 as an orderless product of orderless sums^{[104]}**1926**= pentagonal number^{[71]}**1927**= 2^{11}- 11^{2}^{[384]}**1928**= number of distinct values taken by 2^2^...^2 (with 13 2's and parentheses inserted in all possible ways)^{[385]}**1929**= Mertens function zero, number of integer partitions of 42 whose distinct parts are connected^{[214]}**1930**= number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most 53^{[266]}**1931**= Sophie Germain prime**1932**= number of partitions of 40 into prime power parts^{[194]}**1933**= centered heptagonal number,^{[67]}Honaker prime^{[207]}**1934**= sum of totient function for first 79 integers**1935**= number of edges in the join of two cycle graphs, both of order 43^{[135]}**1936**= 44^{2}, 18-gonal number,^{[386]}324-gonal number.**1937**= number of chiral n-ominoes in 12-space, one cell labeled^{[387]}**1938**= Mertens function zero, number of points on surface of octahedron with edgelength 22^{[139]}**1939**= 7-Knödel number^{[123]}**1940**= the Mahonian number: T(8, 9)^{[175]}**1941**= maximal number of regions obtained by joining 16 points around a circle by straight lines^{[388]}**1942**= number k for which 10k + 1, 10k + 3, 10k + 7, 10k + 9 and 10k + 13 are primes^{[389]}**1943**= largest number not the sum of distinct tetradecagonal numbers^{[390]}**1944**= 3-smooth number (2^{3}×3^{5}), Achilles number^{[275]}**1945**= number of partitions of 25 into relatively prime parts such that multiplicities of parts are also relatively prime^{[391]}**1946**= number of surface points on a cube with edge-length 19^{[20]}**1947**= k such that 5·2^{k}+ 1 is a prime factor of a Fermat number 2^{2m}+ 1 for some m^{[392]}**1948**= number of strict solid partitions of 20^{[87]}**1949**= smallest prime > 44^{2}.^{[142]}**1950**= [math]\displaystyle{ 1 \cdot 2 \cdot 3 + 4 \cdot 5 \cdot 6 + 7 \cdot 8 \cdot 9 + 10 \cdot 11 \cdot 12 }[/math],^{[393]}largest number not the sum of distinct pentadecagonal numbers^{[390]}**1951**= cuban prime^{[293]}**1952**= number of covers of {1, 2, 3, 4}^{[394]}**1953**= triangular number**1956**= number of sum-free subsets of {1, ..., 16}^{[242]}**1955**= number of partitions of 25 with at least one distinct part^{[186]}**1956**= nonagonal number^{[169]}**1957**= [math]\displaystyle{ \sum_{k=0}^{6} \frac{6!}{k!} }[/math] = total number of ordered k-tuples (k=0,1,2,3,4,5,6) of distinct elements from an 6-element set^{[395]}**1958**= number of partitions of 25^{[188]}**1959**= Heptanacci-Lucas number^{[396]}**1960**= number of parts in all partitions of 33 into distinct parts^{[46]}**1961**= number of lattice points inside a circle of radius 25^{[113]}**1962**= number of edges in the join of the complete graph K_{36}and the cycle graph C_{36}^{[397]}**1963**! - 1 is prime^{[398]}**1964**= number of linear forests of planted planar trees with 8 nodes^{[399]}**1965**= total number of parts in all partitions of 17^{[63]}**1966**= sum of totient function for first 80 integers**1967**= least edge-length of a square dissectable into at least 30 squares in the Mrs. Perkins's quilt problem^{[400]}**σ(1968)**= σ(1967) + σ(1966)^{[401]}**1969**= Only value less than four million for which a "mod-ification" of the standard Ackermann Function does not stabilize^{[402]}**1970**= number of compositions of two types of 9 having no even parts^{[403]}**1971**= [math]\displaystyle{ 3^7-6^3 }[/math]^{[404]}**1972**= n such that [math]\displaystyle{ \frac{n^{37}-1}{n-1} }[/math] is prime^{[405]}-
**1973**= Sophie Germain prime, Leonardo prime **1974**= number of binary vectors of length 17 containing no singletons^{[170]}**1975**= number of partitions of 28 with nonnegative rank^{[281]}**1976**= octagonal number^{[141]}**1977**= number of non-isomorphic multiset partitions of weight 9 with no singletons^{[406]}**1978**= n such that n | (3^{n}+ 5)^{[407]}**1979**= number of squares between 45^{2}and 45^{4}.^{[109]}**1980**= pronic number^{[52]}**1981**= pinwheel number^{[91]}**1982**= maximal number of regions the plane is divided into by drawing 45 circles^{[191]}**1983**= skiponacci number^{[114]}**1984**= 11111000000 in binary, see also: 1984 (disambiguation)**1985**= centered square number^{[16]}**1986**= number of ways to write 25 as an orderless product of orderless sums^{[104]}**1987**= 300th prime number**1988**= sum of the first 33 primes**1989**= number of 9-step mappings with 4 inputs^{[236]}**1990**= Stella octangula number**1991**= 11 × 181, the 46th Gullwing number,^{[408]}palindromic composite number with only palindromic prime factors^{[409]}**1992**= number of nonisomorphic sets of nonempty subsets of a 4-set^{[410]}**1993**= a number with the property that 4^{1993}- 3^{1993}is prime,^{[411]}number of partitions of 30 into a prime number of parts^{[105]}**1994**= Glaisher's function W(37)^{[412]}**1995**= number of unlabeled graphs on 9 vertices with independence number 6^{[413]}**1996**= a number with the property that (1996! + 3)/3 is prime^{[414]}**1997**= [math]\displaystyle{ \sum_{k=1}^{21} {k \cdot \phi(k)} }[/math]^{[415]}**1998**= triangular matchstick number^{[49]}**1999**= centered triangular number^{[416]}number of regular forms in a myriagram.

### Prime numbers

There are 135 prime numbers between 1000 and 2000:^{[417]}^{[418]}

- 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999

## References

- ↑ "chiliad". Merriam-Webster. https://www.merriam-webster.com/dictionary/chiliad.
- ↑ Caldwell, Chris K (2021). "The First 1,000 Primes". University of Tennessee at Martin. https://primes.utm.edu/lists/small/1000.txt.
- ↑ Sloane, N. J. A., ed. "Sequence A051876 (24-gonal numbers.)". OEIS Foundation. https://oeis.org/A051876. Retrieved 2022-11-30.
- ↑ "1000". Prime Curious!. https://primes.utm.edu/curios/page.php/1000.html.
- ↑ "Sloane's A122189 : Heptanacci numbers". OEIS Foundation. https://oeis.org/A122189.
- ↑ Sloane, N. J. A., ed. "Sequence A007585 (10-gonal (or decagonal) pyramidal numbers)". OEIS Foundation. https://oeis.org/A007585. Retrieved 2022-05-24.
- ↑ Sloane, N. J. A., ed. "Sequence A332307 (Array read by antidiagonals: T(m,n) is the number of (undirected) Hamiltonian paths in the m X n grid graph)". OEIS Foundation. https://oeis.org/A332307. Retrieved 2023-01-08.
- ↑ Sloane, N. J. A., ed. "Sequence A036063 (Increasing gaps among twin primes: size)". OEIS Foundation. https://oeis.org/A036063. Retrieved 2023-01-08.
- ↑
^{9.0}^{9.1}"A003352 - Oeis". https://oeis.org/A003352. - ↑ Sloane, N. J. A., ed. "Sequence A061341 (A061341 Numbers not ending in 0 whose cubes are concatenations of other cubes)". OEIS Foundation. https://oeis.org/A061341. Retrieved 2023-01-08.
- ↑ "A003353 - Oeis". https://oeis.org/A003353.
- ↑ Sloane, N. J. A., ed. "Sequence A034262 (n^3 + n)". OEIS Foundation. https://oeis.org/A034262. Retrieved 2022-05-24.
- ↑
^{13.0}^{13.1}Sloane, N. J. A., ed. "Sequence A020473 (Egyptian fractions: number of partitions of 1 into reciprocals of positive integers < n+1)". OEIS Foundation. https://oeis.org/A020473. Retrieved 2022-05-24. - ↑ "A046092 - Oeis". https://oeis.org/A046092.
- ↑
^{15.00}^{15.01}^{15.02}^{15.03}^{15.04}^{15.05}^{15.06}^{15.07}^{15.08}^{15.09}^{15.10}^{15.11}^{15.12}^{15.13}^{15.14}"Sloane's A005384 : Sophie Germain primes". OEIS Foundation. https://oeis.org/A005384. - ↑
^{16.0}^{16.1}^{16.2}^{16.3}^{16.4}^{16.5}^{16.6}^{16.7}^{16.8}^{16.9}"Sloane's A001844 : Centered square numbers". OEIS Foundation. https://oeis.org/A001844. - ↑ Sloane, N. J. A., ed. "Sequence A000325 (2^n - n)". OEIS Foundation. https://oeis.org/A000325. Retrieved 2022-05-24.
- ↑
^{18.0}^{18.1}^{18.2}^{18.3}"Sloane's A000330 : Square pyramidal numbers". OEIS Foundation. https://oeis.org/A000330. - ↑
^{19.0}^{19.1}^{19.2}^{19.3}^{19.4}^{19.5}^{19.6}^{19.7}"Sloane's A005282 : Mian-Chowla sequence". OEIS Foundation. https://oeis.org/A005282. - ↑
^{20.0}^{20.1}^{20.2}^{20.3}^{20.4}^{20.5}Sloane, N. J. A., ed. "Sequence A005897 (6*n^2 + 2 for n > 0)". OEIS Foundation. https://oeis.org/A005897. - ↑ "A316729 - Oeis". https://oeis.org/A316729.
- ↑ Sloane, N. J. A., ed. "Sequence A006313 (Numbers n such that n^16 + 1 is prime)". OEIS Foundation. https://oeis.org/A006313. Retrieved 2022-05-24.
- ↑
^{23.00}^{23.01}^{23.02}^{23.03}^{23.04}^{23.05}^{23.06}^{23.07}^{23.08}^{23.09}^{23.10}^{23.11}"Sloane's A005385 : Safe primes". OEIS Foundation. https://oeis.org/A005385. - ↑ Sloane, N. J. A., ed. "Sequence A034964 (Sums of five consecutive primes.)". OEIS Foundation. https://oeis.org/A034964. Retrieved 2022-11-01.
- ↑ Sloane, N. J. A., ed. "Sequence A000162 (Number of 3-dimensional polyominoes (or polycubes) with n cells.)". OEIS Foundation. https://oeis.org/A000162. Retrieved 2022-11-01.
- ↑
^{26.0}^{26.1}Sloane, N. J. A., ed. "Sequence A007053 (Number of primes < 2^n+1)". OEIS Foundation. https://oeis.org/A007053. Retrieved 2022-06-02. - ↑ Sloane, N. J. A., ed. "Sequence A004023 (Indices of prime repunits: numbers n such that 11...111 (with n 1's)... is prime)". OEIS Foundation. https://oeis.org/A004023. Retrieved 2023-02-25.
- ↑ "A004801 - Oeis". https://oeis.org/A004801.
- ↑
^{29.0}^{29.1}^{29.2}^{29.3}^{29.4}^{29.5}^{29.6}^{29.7}"Sloane's A000217 : Triangular numbers". OEIS Foundation. https://oeis.org/A000217. - ↑
^{30.0}^{30.1}^{30.2}^{30.3}^{30.4}^{30.5}^{30.6}^{30.7}^{30.8}"Sloane's A000384 : Hexagonal numbers". OEIS Foundation. https://oeis.org/A000384. - ↑
^{31.0}^{31.1}"A000124 - Oeis". https://oeis.org/A000124. - ↑ "A161328 - Oeis". https://oeis.org/A161328.
- ↑ "A023036 - Oeis". https://oeis.org/A023036.
- ↑ "A007522 - Oeis". https://oeis.org/A007522.
- ↑
^{35.0}^{35.1}^{35.2}^{35.3}Sloane, N. J. A., ed. "Sequence A002865 (Number of partitions of n that do not contain 1 as a part)". OEIS Foundation. https://oeis.org/A002865. Retrieved 2022-06-02. - ↑
^{36.0}^{36.1}"A000695 - Oeis". https://oeis.org/A000695. - ↑ "A003356 - Oeis". https://oeis.org/A003356.
- ↑
^{38.0}^{38.1}"A003357 - Oeis". https://oeis.org/A003357. - ↑ "A036301 - Oeis". https://oeis.org/A036301.
- ↑ "A000567 - Oeis". https://oeis.org/A000567.
- ↑ "A000025 - Oeis". https://oeis.org/A000025.
- ↑ "A336130 - Oeis". https://oeis.org/A336130.
- ↑ "A073576 - Oeis". https://oeis.org/A073576.
- ↑
^{44.0}^{44.1}^{44.2}^{44.3}^{44.4}^{44.5}^{44.6}"Sloane's A100827 : Highly cototient numbers". OEIS Foundation. https://oeis.org/A100827. - ↑ "Base converter | number conversion". https://www.rapidtables.com/convert/number/base-converter.html?x=1050&sel1=3&sel2=10.
- ↑
^{46.0}^{46.1}^{46.2}^{46.3}^{46.4}Sloane, N. J. A., ed. "Sequence A015723 (Number of parts in all partitions of n into distinct parts)". OEIS Foundation. https://oeis.org/A015723. - ↑
^{47.0}^{47.1}^{47.2}^{47.3}^{47.4}^{47.5}^{47.6}^{47.7}"Sloane's A005891 : Centered pentagonal numbers". OEIS Foundation. https://oeis.org/A005891. - ↑ "A003365 - Oeis". https://oeis.org/A003365.
- ↑
^{49.00}^{49.01}^{49.02}^{49.03}^{49.04}^{49.05}^{49.06}^{49.07}^{49.08}^{49.09}^{49.10}Sloane, N. J. A., ed. "Sequence A045943 (Triangular matchstick numbers: 3*n*(n+1)/2)". OEIS Foundation. https://oeis.org/A045943. Retrieved 2022-06-02. - ↑ "A005448 - Oeis". https://oeis.org/A005448.
- ↑ "A003368 - Oeis". https://oeis.org/A003368.
- ↑
^{52.00}^{52.01}^{52.02}^{52.03}^{52.04}^{52.05}^{52.06}^{52.07}^{52.08}^{52.09}^{52.10}^{52.11}^{52.12}"Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers". OEIS Foundation. https://oeis.org/A002378. - ↑ "A002061 - Oeis". https://oeis.org/A002061.
- ↑ "A003349 - Oeis". https://oeis.org/A003349.
- ↑
^{55.0}^{55.1}^{55.2}^{55.3}Sloane, N. J. A., ed. "Sequence A001105 (2*n^2)". OEIS Foundation. https://oeis.org/A001105. - ↑ "A003294 - Oeis". https://oeis.org/A003294.
- ↑
^{57.0}^{57.1}^{57.2}"A035137 - Oeis". https://oeis.org/A035137. - ↑ "A347565: Primes p such that A241014(A000720(p)) is +1 or -1". OEIS Foundation. https://oeis.org/A347565.
- ↑ "A003325 - Oeis". https://oeis.org/A003325.
- ↑ "A195162 - Oeis". https://oeis.org/A195162.
- ↑ "A006532 - Oeis". https://oeis.org/A006532.
- ↑ "A341450 - Oeis". https://oeis.org/A341450.
- ↑
^{63.0}^{63.1}^{63.2}Sloane, N. J. A., ed. "Sequence A006128 (Total number of parts in all partitions of n. Also, sum of largest parts of all partitions of n)". OEIS Foundation. https://oeis.org/A006128. - ↑
^{64.0}^{64.1}"A006567 - Oeis". https://oeis.org/A006567. - ↑
^{65.0}^{65.1}"A003354 - Oeis". https://oeis.org/A003354. - ↑
^{66.0}^{66.1}^{66.2}^{66.3}^{66.4}^{66.5}^{66.6}^{66.7}"Sloane's A000566 : Heptagonal numbers". OEIS Foundation. https://oeis.org/A000566. - ↑
^{67.0}^{67.1}^{67.2}^{67.3}^{67.4}^{67.5}^{67.6}"Sloane's A069099 : Centered heptagonal numbers". OEIS Foundation. https://oeis.org/A069099. - ↑ "A273873 - Oeis". https://oeis.org/A273873.
- ↑ "A292457 - Oeis". https://oeis.org/A292457.
- ↑ "A073592 - Oeis". https://oeis.org/A073592.
- ↑
^{71.0}^{71.1}^{71.2}^{71.3}^{71.4}^{71.5}^{71.6}^{71.7}^{71.8}^{71.9}"Sloane's A000326 : Pentagonal numbers". OEIS Foundation. https://oeis.org/A000326. - ↑
^{72.0}^{72.1}^{72.2}"Sloane's A000931 : Padovan sequence". OEIS Foundation. https://oeis.org/A000931. - ↑ "A077043 - Oeis". https://oeis.org/A077043.
- ↑ "A056107 - Oeis". https://oeis.org/A056107.
- ↑ "A025147 - Oeis". https://oeis.org/A025147.
- ↑ "Sloane's A006753 : Smith numbers". OEIS Foundation. https://oeis.org/A006753.
- ↑ "Sloane's A031157 : Numbers that are both lucky and prime". OEIS Foundation. https://oeis.org/A031157.
- ↑ "A033996 - Oeis". https://oeis.org/A033996.
- ↑ "A018900 - Oeis". https://oeis.org/A018900.
- ↑ "A046308 - Oeis". https://oeis.org/A046308.
- ↑ "Sloane's A001232 : Numbers n such that 9*n = (n written backwards)". OEIS Foundation. https://oeis.org/A001232.
- ↑ "A003350 - Oeis". https://oeis.org/A003350.
- ↑ Wells, D.
*The Penguin Dictionary of Curious and Interesting Numbers*London: Penguin Group. (1987): 163 - ↑
^{84.0}^{84.1}^{84.2}^{84.3}^{84.4}"Sloane's A003154 : Centered 12-gonal numbers. Also star numbers". OEIS Foundation. https://oeis.org/A003154. - ↑ "A003355 - Oeis". https://oeis.org/A003355.
- ↑ "A051682 - Oeis". https://oeis.org/A051682.
- ↑
^{87.0}^{87.1}^{87.2}Sloane, N. J. A., ed. "Sequence A323657 (Number of strict solid partitions of n)". OEIS Foundation. https://oeis.org/A323657. - ↑ "A121029 - Oeis". https://oeis.org/A121029.
- ↑ "A292449 - Oeis". https://oeis.org/A292449.
- ↑ Sloane, N. J. A., ed. "Sequence A087188 (number of partitions of n into distinct squarefree parts)". OEIS Foundation. https://oeis.org/A087188.
- ↑
^{91.0}^{91.1}^{91.2}^{91.3}^{91.4}^{91.5}^{91.6}^{91.7}^{91.8}Sloane, N. J. A., ed. "Sequence A059993 (Pinwheel numbers: 2*n^2 + 6*n + 1)". OEIS Foundation. https://oeis.org/A059993. - ↑
^{92.0}^{92.1}^{92.2}^{92.3}^{92.4}^{92.5}^{92.6}^{92.7}^{92.8}"Sloane's A006562 : Balanced primes". OEIS Foundation. https://oeis.org/A006562. - ↑
^{93.0}^{93.1}"Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)". OEIS Foundation. https://oeis.org/A007629. - ↑ "Sloane's A002997 : Carmichael numbers". OEIS Foundation. https://oeis.org/A002997.
- ↑
^{95.0}^{95.1}^{95.2}^{95.3}^{95.4}"Sloane's A001107 : 10-gonal (or decagonal) numbers". OEIS Foundation. https://oeis.org/A001107. - ↑
^{96.0}^{96.1}Sloane, N. J. A., ed. "Sequence A001567 (Fermat pseudoprimes to base 2, also called Sarrus numbers or Poulet numbers)". OEIS Foundation. https://oeis.org/A001567. - ↑
^{97.0}^{97.1}^{97.2}Sloane, N. J. A., ed. "Sequence A051890 (2*(n^2 - n + 1))". OEIS Foundation. https://oeis.org/A051890. - ↑ Sloane, N. J. A., ed. "Sequence A319560 (Number of non-isomorphic strict T_0 multiset partitions of weight n)". OEIS Foundation. https://oeis.org/A319560.
- ↑
^{99.0}^{99.1}^{99.2}Sloane, N. J. A., ed. "Sequence A028916 (Friedlander-Iwaniec primes: Primes of form a^2 + b^4)". OEIS Foundation. https://oeis.org/A028916. - ↑ Sloane, N. J. A., ed. "Sequence A057732 (Numbers k such that 2^k + 3 is prime)". OEIS Foundation. https://oeis.org/A057732.
- ↑
^{101.0}^{101.1}Sloane, N. J. A., ed. "Sequence A046376 (Palindromes with exactly 2 palindromic prime factors (counted with multiplicity), and no other prime factors)". OEIS Foundation. https://oeis.org/A046376. - ↑ Sloane, N. J. A., ed. "Sequence A128455 (Numbers k such that 9^k - 2 is a prime)". OEIS Foundation. https://oeis.org/A128455.
- ↑
^{103.0}^{103.1}^{103.2}^{103.3}^{103.4}Sloane, N. J. A., ed. "Sequence A000009 (Expansion of Product_{m > 0} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts)". OEIS Foundation. https://oeis.org/A000009. - ↑
^{104.0}^{104.1}^{104.2}^{104.3}Sloane, N. J. A., ed. "Sequence A318949 (Number of ways to write n as an orderless product of orderless sums)". OEIS Foundation. https://oeis.org/A318949. - ↑
^{105.0}^{105.1}^{105.2}^{105.3}Sloane, N. J. A., ed. "Sequence A038499 (Number of partitions of n into a prime number of parts)". OEIS Foundation. https://oeis.org/A038499. - ↑
^{106.0}^{106.1}Sloane, N. J. A., ed. "Sequence A006748 (Number of diagonally symmetric polyominoes with n cells)". OEIS Foundation. https://oeis.org/A006748. - ↑
^{107.0}^{107.1}^{107.2}^{107.3}^{107.4}Sloane, N. J. A., ed. "Sequence A210000 (Number of unimodular 2 X 2 matrices having all terms in {0,1,...,n)". OEIS Foundation. https://oeis.org/A210000.} - ↑ Sloane, N. J. A., ed. "Sequence A033995 (Number of bipartite graphs with n nodes)". OEIS Foundation. https://oeis.org/A033995.
- ↑
^{109.0}^{109.1}^{109.2}^{109.3}^{109.4}Sloane, N. J. A., ed. "Sequence A028387 (n + (n+1)^2)". OEIS Foundation. https://oeis.org/A028387. - ↑
^{110.0}^{110.1}^{110.2}^{110.3}^{110.4}"Sloane's A076980 : Leyland numbers". OEIS Foundation. https://oeis.org/A076980. - ↑ Sloane, N. J. A., ed. "Sequence A062801 (Number of 2 X 2 non-singular integer matrices with entries from {0,...,n)". OEIS Foundation. https://oeis.org/A062801.}
- ↑
^{112.0}^{112.1}^{112.2}^{112.3}^{112.4}^{112.5}Sloane, N. J. A., ed. "Sequence A000096 (n*(n+3)/2)". OEIS Foundation. https://oeis.org/A000096. - ↑
^{113.0}^{113.1}^{113.2}^{113.3}^{113.4}^{113.5}^{113.6}Sloane, N. J. A., ed. "Sequence A000328". OEIS Foundation. https://oeis.org/A000328. - ↑
^{114.0}^{114.1}^{114.2}Sloane, N. J. A., ed. "Sequence A001608 (Perrin sequence)". OEIS Foundation. https://oeis.org/A001608. - ↑
^{115.0}^{115.1}^{115.2}^{115.3}^{115.4}^{115.5}Sloane, N. J. A., ed. "Sequence A140091 (3*n*(n + 3)/2)". OEIS Foundation. https://oeis.org/A140091. - ↑ Sloane, N. J. A., ed. "Sequence A005380". OEIS Foundation. https://oeis.org/A005380.
- ↑ Sloane, N. J. A., ed. "Sequence A051026 (Number of primitive subsequences of 1, 2, ..., n)". OEIS Foundation. https://oeis.org/A051026.
- ↑
^{118.0}^{118.1}^{118.2}^{118.3}^{118.4}^{118.5}^{118.6}^{118.7}^{118.8}Sloane, N. J. A., ed. "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". OEIS Foundation. https://oeis.org/A005448. - ↑ Sloane, N. J. A., ed. "Sequence A080040 (2*a(n-1) + 2*a(n-2) for n > 1)". OEIS Foundation. https://oeis.org/A080040.
- ↑ Sloane, N. J. A., ed. "Sequence A264237 (Sum of values of vertices at level n of the hyperbolic Pascal pyramid)". OEIS Foundation. https://oeis.org/A264237.
- ↑
^{121.0}^{121.1}Sloane, N. J. A., ed. "Sequence A033991 (n*(4*n-1))". OEIS Foundation. https://oeis.org/A033991. - ↑ "Sloane's A000292 : Tetrahedral numbers". OEIS Foundation. https://oeis.org/A000292.
- ↑
^{123.0}^{123.1}^{123.2}^{123.3}^{123.4}^{123.5}Sloane, N. J. A., ed. "Sequence A208155 (7-Knödel numbers)". OEIS Foundation. https://oeis.org/A208155. - ↑
^{124.0}^{124.1}^{124.2}^{124.3}^{124.4}Sloane, N. J. A., ed. "Sequence A006315 (Numbers n such that n^32 + 1 is prime)". OEIS Foundation. https://oeis.org/A006315. - ↑ Sloane, N. J. A., ed. "Sequence A185982 (Triangle read by rows: number of set partitions of n elements with k connectors)". OEIS Foundation. https://oeis.org/A185982.
- ↑
^{126.0}^{126.1}^{126.2}^{126.3}Sloane, N. J. A., ed. "Sequence A007534 (Even numbers that are not the sum of a pair of twin primes)". OEIS Foundation. https://oeis.org/A007534. - ↑
^{127.0}^{127.1}^{127.2}^{127.3}^{127.4}Sloane, N. J. A., ed. "Sequence A050993 (5-Knödel numbers)". OEIS Foundation. https://oeis.org/A050993. - ↑ Sloane, N. J. A., ed. "Sequence A006094 (Products of 2 successive primes)". OEIS Foundation. https://oeis.org/A006094.
- ↑ Sloane, N. J. A., ed. "Sequence A046368 (Products of two palindromic primes)". OEIS Foundation. https://oeis.org/A046368.
- ↑ "1150 (number)". https://number.academy/1150.
- ↑
^{131.0}^{131.1}"Sloane's A000101 : Increasing gaps between primes (upper end)". OEIS Foundation. https://oeis.org/A000101. - ↑
^{132.0}^{132.1}"Sloane's A097942 : Highly totient numbers". OEIS Foundation. https://oeis.org/A097942. - ↑
^{133.0}^{133.1}^{133.2}^{133.3}"Sloane's A080076 : Proth primes". OEIS Foundation. https://oeis.org/A080076. - ↑
^{134.0}^{134.1}^{134.2}^{134.3}^{134.4}^{134.5}Sloane, N. J. A., ed. "Sequence A005893 (Number of points on surface of tetrahedron; coordination sequence for sodalite net (equals 2*n^2+2 for n > 0))". OEIS Foundation. https://oeis.org/A005893. - ↑
^{135.0}^{135.1}^{135.2}^{135.3}^{135.4}^{135.5}^{135.6}^{135.7}^{135.8}^{135.9}Sloane, N. J. A., ed. "Sequence n*(n+2)". OEIS Foundation. https://oeis.org/n*(n+2). - ↑
^{136.0}^{136.1}^{136.2}"Sloane's A005900 : Octahedral numbers". OEIS Foundation. https://oeis.org/A005900. - ↑ "Sloane's A069125 : a(n) = (11*n^2 - 11*n + 2)/2". OEIS Foundation. https://oeis.org/A069125.
- ↑ "1157 (number)". https://number.academy/1157.
- ↑
^{139.0}^{139.1}^{139.2}^{139.3}^{139.4}Sloane, N. J. A., ed. "Sequence A005899 (Number of points on surface of octahedron)". OEIS Foundation. https://oeis.org/A005899. - ↑
^{140.0}^{140.1}Sloane, N. J. A., ed. "Sequence A001845 (Centered octahedral numbers (crystal ball sequence for cubic lattice))". OEIS Foundation. https://oeis.org/A001845. Retrieved 2022-06-02. - ↑
^{141.0}^{141.1}^{141.2}^{141.3}^{141.4}Sloane, N. J. A., ed. "Sequence A000567 (Octagonal numbers: n*(3*n-2). Also called star numbers)". OEIS Foundation. https://oeis.org/A000567. - ↑
^{142.0}^{142.1}^{142.2}^{142.3}Sloane, N. J. A., ed. "Sequence A007491 (Smallest prime > n^2)". OEIS Foundation. https://oeis.org/A007491. - ↑
^{143.0}^{143.1}^{143.2}Sloane, N. J. A., ed. "Sequence A002413 (Heptagonal (or 7-gonal) pyramidal numbers)". OEIS Foundation. https://oeis.org/A002413. - ↑
^{144.0}^{144.1}^{144.2}^{144.3}Sloane, N. J. A., ed. "Sequence A018805". OEIS Foundation. https://oeis.org/A018805. - ↑ "A063776 - OEIS". https://oeis.org/A063776.
- ↑ "A000256 - OEIS". https://oeis.org/A000256.
- ↑ "1179 (number)". https://number.academy/1179.
- ↑ "A000339 - OEIS". https://oeis.org/A000339.
- ↑ "A271269 - OEIS". https://oeis.org/A271269.
- ↑ "A000031 - OEIS". https://oeis.org/A000031.
- ↑ Higgins, Peter (2008).
*Number Story: From Counting to Cryptography*. New York: Copernicus. p. 61. ISBN 978-1-84800-000-1. https://archive.org/details/numberstoryfromc00higg_612. - ↑
^{152.0}^{152.1}^{152.2}^{152.3}^{152.4}Sloane, N. J. A., ed. "Sequence A051424 (Number of partitions of n into pairwise relatively prime parts)". OEIS Foundation. https://oeis.org/A051424. - ↑
^{153.0}^{153.1}"Sloane's A042978 : Stern primes". OEIS Foundation. https://oeis.org/A042978. - ↑ "A121038 - OEIS". https://oeis.org/A121038.
- ↑
^{155.0}^{155.1}Sloane, N. J. A., ed. "Sequence A005449 (Second pentagonal numbers: n*(3*n + 1)/2)". OEIS Foundation. https://oeis.org/A005449. - ↑
^{156.0}^{156.1}^{156.2}^{156.3}^{156.4}^{156.5}Sloane, N. J. A., ed. "Sequence A002061 (Central polygonal numbers: n^2 - n + 1)". OEIS Foundation. https://oeis.org/A002061. - ↑ "A175654 - OEIS". https://oeis.org/A175654.
- ↑ oeis.org/A062092
- ↑
^{159.0}^{159.1}^{159.2}^{159.3}^{159.4}^{159.5}Sloane, N. J. A., ed. "Sequence A024916 (Sum_1^n sigma(k))". OEIS Foundation. https://oeis.org/A024916. - ↑
^{160.0}^{160.1}^{160.2}^{160.3}^{160.4}>Sloane, N. J. A., ed. "Sequence A080663 (3*n^2 - 1)". OEIS Foundation. https://oeis.org/A080663. - ↑ Meehan, Eileen R.,
*Why TV is not our fault: television programming, viewers, and who's really in control*Lanham, MD: Rowman & Littlefield, 2005 - ↑ "A265070 - OEIS". https://oeis.org/A265070.
- ↑ "1204 (number)". https://number.academy/1204.
- ↑
^{164.0}^{164.1}Sloane, N. J. A., ed. "Sequence A240574 (Number of partitions of n such that the number of odd parts is a part)". OEIS Foundation. https://oeis.org/A240574. - ↑ "A303815 - OEIS". https://oeis.org/A303815.
- ↑
^{166.0}^{166.1}^{166.2}^{166.3}^{166.4}^{166.5}^{166.6}^{166.7}Sloane, N. J. A., ed. "Sequence A098237 (Composite de Polignac numbers)". OEIS Foundation. https://oeis.org/A098237. - ↑ Higgins, ibid.
- ↑
^{168.0}^{168.1}^{168.2}^{168.3}^{168.4}^{168.5}^{168.6}^{168.7}^{168.8}Sloane, N. J. A., ed. "Sequence A053767 (Sum of first n composite numbers)". OEIS Foundation. https://oeis.org/A053767. - ↑
^{169.0}^{169.1}^{169.2}^{169.3}^{169.4}^{169.5}"Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". OEIS Foundation. https://oeis.org/A001106. - ↑
^{170.0}^{170.1}Sloane, N. J. A., ed. "Sequence A006355 (Number of binary vectors of length n containing no singletons)". OEIS Foundation. https://oeis.org/A006355. - ↑ "Sloane's A001110 : Square triangular numbers". OEIS Foundation. https://oeis.org/A001110.
- ↑
^{172.0}^{172.1}^{172.2}^{172.3}^{172.4}"Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers". OEIS Foundation. https://oeis.org/A016754. - ↑ "A004111 - OEIS". https://oeis.org/A004111.
- ↑ "A061262 - OEIS". https://oeis.org/A061262.
- ↑
^{175.0}^{175.1}^{175.2}Sloane, N. J. A., ed. "Sequence A008302 (Triangle of Mahonian numbers T(n,k): coefficients in expansion of Product{0..n-1} (1 + x + ... + x^i), where k ranges from 0 to A000217(n-1). Also enumerates permutations by their major index)". OEIS Foundation. https://oeis.org/A008302. - ↑ "A006154 - OEIS". https://oeis.org/A006154.
- ↑ "A000045 - OEIS". https://oeis.org/A000045.
- ↑
^{178.0}^{178.1}^{178.2}^{178.3}^{178.4}^{178.5}^{178.6}Sloane, N. J. A., ed. "Sequence A054735 (Sums of twin prime pairs)". OEIS Foundation. https://oeis.org/A054735. - ↑ "A160160 - OEIS". https://oeis.org/A160160.
- ↑ "Sloane's A005898 : Centered cube numbers". OEIS Foundation. https://oeis.org/A005898.
- ↑ Sloane, N. J. A., ed. "Sequence A126796 (Number of complete partitions of n)". OEIS Foundation. https://oeis.org/A126796.
- ↑ oeis.org/A305843
- ↑ "A007690 - OEIS". https://oeis.org/A007690.
- ↑ "Sloane's A033819 : Trimorphic numbers". OEIS Foundation. https://oeis.org/A033819.
- ↑
^{185.0}^{185.1}^{185.2}^{185.3}Sloane, N. J. A., ed. "Sequence A058331 (2*n^2 + 1)". OEIS Foundation. https://oeis.org/A058331. - ↑
^{186.0}^{186.1}^{186.2}Sloane, N. J. A., ed. "Sequence A144300 (Number of partitions of n minus number of divisors of n)". OEIS Foundation. https://oeis.org/A144300. - ↑ Sloane, N. J. A., ed. "Sequence A000837 (Number of partitions of n into relatively prime parts. Also aperiodic partitions.)". OEIS Foundation. https://oeis.org/A000837.
- ↑
^{188.0}^{188.1}^{188.2}Sloane, N. J. A., ed. "Sequence A000041 (a(n) is the number of partitions of n (the partition numbers))". OEIS Foundation. https://oeis.org/A000041. - ↑
^{189.0}^{189.1}"Sloane's A002182 : Highly composite numbers". OEIS Foundation. https://oeis.org/A002182. - ↑
^{190.0}^{190.1}^{190.2}^{190.3}^{190.4}"Sloane's A014575 : Vampire numbers". OEIS Foundation. https://oeis.org/A014575. - ↑
^{191.0}^{191.1}^{191.2}^{191.3}^{191.4}^{191.5}^{191.6}^{191.7}^{191.8}^{191.9}Sloane, N. J. A., ed. "Sequence A014206 (n^2 + n + 2)". OEIS Foundation. https://oeis.org/A014206. - ↑
^{192.0}^{192.1}Sloane, N. J. A., ed. "Sequence A070169 (Rounded total surface area of a regular tetrahedron with edge length n)". OEIS Foundation. https://oeis.org/A070169. - ↑
^{193.0}^{193.1}^{193.2}Sloane, N. J. A., ed. "Sequence A003238 (Number of rooted trees with n vertices in which vertices at the same level have the same degree)". OEIS Foundation. https://oeis.org/A003238. - ↑
^{194.0}^{194.1}^{194.2}Sloane, N. J. A., ed. "Sequence A023894 (Number of partitions of n into prime power parts)". OEIS Foundation. https://oeis.org/A023894. - ↑
^{195.0}^{195.1}^{195.2}Sloane, N. J. A., ed. "Sequence A072895 (Least k for the Theodorus spiral to complete n revolutions)". OEIS Foundation. https://oeis.org/A072895. - ↑ Sloane, N. J. A., ed. "Sequence A100040 (2*n^2 + n - 5)". OEIS Foundation. https://oeis.org/A100040.
- ↑ Sloane, N. J. A., ed. "Sequence A051349 (Sum of first n nonprimes)". OEIS Foundation. https://oeis.org/A051349.
- ↑ Sloane, N. J. A., ed. "Sequence A033286 (n * prime(n))". OEIS Foundation. https://oeis.org/A033286.
- ↑
^{199.0}^{199.1}Sloane, N. J. A., ed. "Sequence A084849 (1 + n + 2*n^2)". OEIS Foundation. https://oeis.org/A084849. - ↑
^{200.0}^{200.1}Sloane, N. J. A., ed. "Sequence A000930 (Narayana's cows sequence)". OEIS Foundation. https://oeis.org/A000930. - ↑ Sloane, N. J. A., ed. "Sequence A001792 ((n+2)*2^(n-1))". OEIS Foundation. https://oeis.org/A001792.
- ↑ Sloane, N. J. A., ed. "Sequence A006958 (Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused))". OEIS Foundation. https://oeis.org/A006958.
- ↑ Sloane, N. J. A., ed. "Sequence A216492 (Number of inequivalent connected planar figures that can be formed from n 1 X 2 rectangles (or dominoes) such that each pair of touching rectangles shares exactly one edge, of length 1, and the adjacency graph of the rectangles is a tree)". OEIS Foundation. https://oeis.org/A216492.
- ↑ Sloane, N. J. A., ed. "Sequence A007318 (Pascal's triangle read by rows)". OEIS Foundation. https://oeis.org/A007318.
- ↑
^{205.0}^{205.1}Sloane, N. J. A., ed. "Sequence A071400 (Rounded volume of a regular octahedron with edge length n)". OEIS Foundation. https://oeis.org/A071400. - ↑
^{206.0}^{206.1}^{206.2}^{206.3}Sloane, N. J. A., ed. "Sequence A003114 (Number of partitions of n into parts 5k+1 or 5k+4)". OEIS Foundation. https://oeis.org/A003114. - ↑
^{207.0}^{207.1}^{207.2}^{207.3}^{207.4}^{207.5}Sloane, N. J. A., ed. "Sequence A033548 (Honaker primes: primes P(k) such that sum of digits of P(k) equals sum of digits of k)". OEIS Foundation. https://oeis.org/A033548. - ↑ Sloane, N. J. A., ed. "Sequence A000055 (Number of trees with n unlabeled nodes)". OEIS Foundation. https://oeis.org/A000055.
- ↑ "A124826 - OEIS". https://oeis.org/A124826.
- ↑ "A142005 - OEIS". https://oeis.org/A142005.
- ↑
^{211.0}^{211.1}Sloane, N. J. A., ed. "Sequence A338470 (Number of integer partitions of n with no part dividing all the others)". OEIS Foundation. https://oeis.org/A338470. - ↑ "Constitutional Court allows 'FCK CPS' sticker".
*The Local*. 28 April 2015. http://www.thelocal.de/20150428/fck-cps-high-court-agrees. ""...state court in Karlsruhe ruled that a banner ... that read 'ACAB' – an abbreviation of 'all cops are bastards' ... a punishable insult. ... A court in Frankfurt ... the numbers '1312' constituted an insult ... the numerals stand for the letters ACAB's position in the alphabet." - ↑ "A066186 - OEIS". https://oeis.org/A066186.
- ↑
^{214.0}^{214.1}^{214.2}^{214.3}Sloane, N. J. A., ed. "Sequence A304716 (Number of integer partitions of n whose distinct parts are connected)". OEIS Foundation. https://oeis.org/A304716. - ↑ "A115073 - OEIS". https://oeis.org/A115073.
- ↑ "A061256 - OEIS". https://oeis.org/A061256.
- ↑ "A061954 - OEIS". https://oeis.org/A061954.
- ↑ "A030299 - OEIS". https://oeis.org/A030299.
- ↑
^{219.0}^{219.1}"Sloane's A002559 : Markoff (or Markov) numbers". OEIS Foundation. https://oeis.org/A002559. - ↑
^{220.0}^{220.1}Sloane, N. J. A., ed. "Sequence A005894 (Centered tetrahedral numbers)". OEIS Foundation. https://oeis.org/A005894. - ↑ "A005064 - OEIS". https://oeis.org/A005064.
- ↑
^{222.0}^{222.1}^{222.2}^{222.3}^{222.4}^{222.5}Sloane, N. J. A., ed. "Sequence A001770 (Numbers k such that 5*2^k - 1 is prime)". OEIS Foundation. https://oeis.org/A001770. - ↑
^{223.0}^{223.1}^{223.2}^{223.3}^{223.4}Sloane, N. J. A., ed. "Sequence A144391 (3*n^2 + n - 1)". OEIS Foundation. https://oeis.org/A144391. - ↑
^{224.0}^{224.1}^{224.2}^{224.3}^{224.4}^{224.5}^{224.6}Sloane, N. J. A., ed. "Sequence A090781 (Numbers that can be expressed as the difference of the squares of primes in just one distinct way)". OEIS Foundation. https://oeis.org/A090781. - ↑
^{225.0}^{225.1}Sloane, N. J. A., ed. "Sequence A056809 (Numbers k such that k, k+1 and k+2 are products of two primes)". OEIS Foundation. https://oeis.org/A056809. - ↑ "A316473 - OEIS". https://oeis.org/A316473.
- ↑ "A000032 - OEIS". https://oeis.org/A000032.
- ↑ "1348 (number)". https://number.academy/1348.
- ↑
^{229.0}^{229.1}Sloane, N. J. A., ed. "Sequence A101624 (Stern-Jacobsthal number)". OEIS Foundation. https://oeis.org/A101624. - ↑
^{230.0}^{230.1}^{230.2}Sloane, N. J. A., ed. "Sequence A000603". OEIS Foundation. https://oeis.org/A000603. - ↑
^{231.0}^{231.1}^{231.2}^{231.3}^{231.4}Sloane, N. J. A., ed. "Sequence A330224 (Number of achiral integer partitions of n)". OEIS Foundation. https://oeis.org/A330224. - ↑
^{232.0}^{232.1}"Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24". OEIS Foundation. https://oeis.org/A000332. - ↑
^{233.0}^{233.1}^{233.2}Sloane, N. J. A., ed. "Sequence A001157 (sigma_2(n): sum of squares of divisors of n)". OEIS Foundation. https://oeis.org/A001157. - ↑
^{234.0}^{234.1}Sloane, N. J. A., ed. "Sequence A007585 (10-gonal (or decagonal) pyramidal numbers)". OEIS Foundation. https://oeis.org/A007585. - ↑
^{235.0}^{235.1}^{235.2}Sloane, N. J. A., ed. "Sequence A071395 (Primitive abundant numbers (abundant numbers all of whose proper divisors are deficient numbers))". OEIS Foundation. https://oeis.org/A071395. - ↑
^{236.0}^{236.1}Sloane, N. J. A., ed. "Sequence A005945 (Number of n-step mappings with 4 inputs)". OEIS Foundation. https://oeis.org/A005945. - ↑ https://oeis.org/A001631
- ↑ Sloane, N. J. A., ed. "Sequence A000111 (Euler or up/down numbers: e.g.f. sec(x) + tan(x))". OEIS Foundation. https://oeis.org/A000111.
- ↑ Sloane, N. J. A., ed. "Sequence A002414 (Octagonal pyramidal numbers)". OEIS Foundation. https://oeis.org/A002414.
- ↑ "Sloane's A001567 : Fermat pseudoprimes to base 2". OEIS Foundation. https://oeis.org/A001567.
- ↑ "Sloane's A050217 : Super-Poulet numbers". OEIS Foundation. https://oeis.org/A050217.
- ↑
^{242.0}^{242.1}Sloane, N. J. A., ed. "Sequence A007865 (Number of sum-free subsets of {1, ..., n)". OEIS Foundation. https://oeis.org/A007865.} - ↑
^{243.0}^{243.1}Sloane, N. J. A., ed. "Sequence A325349 (Number of integer partitions of n whose augmented differences are distinct)". OEIS Foundation. https://oeis.org/A325349. - ↑ "Sloane's A000682 : Semimeanders". OEIS Foundation. https://oeis.org/A000682.
- ↑
^{245.0}^{245.1}Sloane, N. J. A., ed. "Sequence A050710 (Smallest composite that when added to sum of prime factors reaches a prime after n iterations)". OEIS Foundation. https://oeis.org/A050710. - ↑
^{246.0}^{246.1}Sloane, N. J. A., ed. "Sequence A067538 (Number of partitions of n in which the number of parts divides n)". OEIS Foundation. https://oeis.org/A067538. - ↑
^{247.0}^{247.1}"Sloane's A051015 : Zeisel numbers". OEIS Foundation. https://oeis.org/A051015. - ↑
^{248.0}^{248.1}Sloane, N. J. A., ed. "Sequence A061068 (Primes which are the sum of a prime and its subscript)". OEIS Foundation. https://oeis.org/A061068. - ↑ "Sloane's A000108 : Catalan numbers". OEIS Foundation. https://oeis.org/A000108.
- ↑
^{250.0}^{250.1}Sloane, N. J. A., ed. "Sequence A071399 (Rounded volume of a regular tetrahedron with edge length n)". OEIS Foundation. https://oeis.org/A071399. - ↑
^{251.0}^{251.1}Sloane, N. J. A., ed. "Sequence A003037 (Smallest number of complexity n: smallest number requiring n 1's to build using +, * and ^)". OEIS Foundation. https://oeis.org/A003037. - ↑
^{252.0}^{252.1}Sloane, N. J. A., ed. "Sequence A062325 (Numbers k for which phi(prime(k)) is a square)". OEIS Foundation. https://oeis.org/A062325. - ↑
^{253.0}^{253.1}Sloane, N. J. A., ed. "Sequence A011379 (n^2*(n+1))". OEIS Foundation. https://oeis.org/A011379. - ↑
^{254.0}^{254.1}Sloane, N. J. A., ed. "Sequence A005918 (Number of points on surface of square pyramid: 3*n^2 + 2 (n>0))". OEIS Foundation. https://oeis.org/A005918. - ↑
^{255.0}^{255.1}^{255.2}^{255.3}^{255.4}^{255.5}^{255.6}Sloane, N. J. A., ed. "Sequence A011257 (Geometric mean of phi(n) and sigma(n) is an integer)". OEIS Foundation. https://oeis.org/A011257. - ↑
^{256.0}^{256.1}Sloane, N. J. A., ed. "Sequence A056220 (2*n^2 - 1)". OEIS Foundation. https://oeis.org/A056220. - ↑ Sloane, N. J. A., ed. "Sequence A028569 (n*(n + 9))". OEIS Foundation. https://oeis.org/A028569.
- ↑ Sloane, N. J. A., ed. "Sequence A071398 (Rounded total surface area of a regular icosahedron with edge length n)". OEIS Foundation. https://oeis.org/A071398.
- ↑
^{259.0}^{259.1}"Sloane's A002411 : Pentagonal pyramidal numbers". OEIS Foundation. https://oeis.org/A002411. - ↑
^{260.0}^{260.1}^{260.2}^{260.3}Sloane, N. J. A., ed. "Sequence A307958 (Coreful perfect numbers)". OEIS Foundation. https://oeis.org/A307958. - ↑ Sloane, N. J. A., ed. "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". OEIS Foundation. https://oeis.org/A000219.
- ↑ Sloane, N. J. A., ed. "Sequence A006330 (Number of corners, or planar partitions of n with only one row and one column)". OEIS Foundation. https://oeis.org/A006330.
- ↑ "Sloane's A000078 : Tetranacci numbers". OEIS Foundation. https://oeis.org/A000078.
- ↑
^{264.0}^{264.1}Sloane, N. J. A., ed. "Sequence A034296 (Number of flat partitions of n)". OEIS Foundation. https://oeis.org/A034296. - ↑
^{265.0}^{265.1}Sloane, N. J. A., ed. "Sequence A084647 (Hypotenuses for which there exist exactly 3 distinct integer triangles)". OEIS Foundation. https://oeis.org/A084647. - ↑
^{266.0}^{266.1}Sloane, N. J. A., ed. "Sequence A002071 (Number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most the n-th prime)". OEIS Foundation. https://oeis.org/A002071. - ↑
^{267.0}^{267.1}Sloane, N. J. A., ed. "Sequence A000702 (number of conjugacy classes in the alternating group A_n)". OEIS Foundation. https://oeis.org/A000702. - ↑ Sloane, N. J. A., ed. "Sequence A071396 (Rounded total surface area of a regular octahedron with edge length n)". OEIS Foundation. https://oeis.org/A071396.
- ↑ Sloane, N. J. A., ed. "Sequence A000615 (Threshold functions of exactly n variables)". OEIS Foundation. https://oeis.org/A000615.
- ↑ Sloane, N. J. A., ed. "Sequence A319066 (Number of partitions of integer partitions of n where all parts have the same length)". OEIS Foundation. https://oeis.org/A319066.
- ↑
^{271.0}^{271.1}^{271.2}^{271.3}Sloane, N. J. A., ed. "Sequence A065381 (Primes not of the form p + 2^k)". OEIS Foundation. https://oeis.org/A065381. - ↑
^{272.0}^{272.1}Sloane, N. J. A., ed. "Sequence A008406 (Triangle T(n,k) read by rows, giving number of graphs with n nodes and k edges))". OEIS Foundation. https://oeis.org/A008406. - ↑ Sloane, N. J. A., ed. "Sequence A000014 (Number of series-reduced trees with n nodes)". OEIS Foundation. https://oeis.org/A000014.
- ↑ Sloane, N. J. A., ed. "Sequence A088319 (Ordered hypotenuses of primitive Pythagorean triangles having legs that add up to a square)". OEIS Foundation. https://oeis.org/A088319.
- ↑
^{275.0}^{275.1}Sloane, N. J. A., ed. "Sequence A052486 (Achilles numbers)". OEIS Foundation. https://oeis.org/A052486. - ↑ "Sloane's A005231 : Odd abundant numbers". OEIS Foundation. https://oeis.org/A005231.
- ↑ Sloane, N. J. A., ed. "Sequence A071402 (Rounded volume of a regular icosahedron with edge length n)". OEIS Foundation. https://oeis.org/A071402.
- ↑ Sloane, N. J. A., ed. "Sequence A006327 (Fibonacci(n) - 3. Number of total preorders)". OEIS Foundation. https://oeis.org/A006327.
- ↑ "Sloane's A000045 : Fibonacci numbers". OEIS Foundation. https://oeis.org/A000045.
- ↑ Sloane, N. J. A., ed. "Sequence A100145 (Structured great rhombicosidodecahedral numbers)". OEIS Foundation. https://oeis.org/A100145.
- ↑
^{281.0}^{281.1}Sloane, N. J. A., ed. "Sequence A064174 (Number of partitions of n with nonnegative rank)". OEIS Foundation. https://oeis.org/A064174. - ↑ Sloane, N. J. A., ed. "Sequence A007584 (9-gonal (or enneagonal) pyramidal numbers)". OEIS Foundation. https://oeis.org/A007584.
- ↑
^{283.0}^{283.1}Sloane, N. J. A., ed. "Sequence A046092 (4 times triangular numbers)". OEIS Foundation. https://oeis.org/A046092. - ↑ Sloane, N. J. A., ed. "Sequence A007290 (2*binomial(n,3))". OEIS Foundation. https://oeis.org/A007290.
- ↑ Sloane, N. J. A., ed. "Sequence A058360 (Number of partitions of n whose reciprocal sum is an integer)". OEIS Foundation. https://oeis.org/A058360.
- ↑ Sloane, N. J. A., ed. "Sequence A046931 (Prime islands: least prime whose adjacent primes are exactly 2n apart)". OEIS Foundation. https://oeis.org/A046931.
- ↑ "Sloane's A001599 : Harmonic or Ore numbers". OEIS Foundation. https://oeis.org/A001599.
- ↑ Sloane, N. J. A., ed. "Sequence A056613 (Number of n-celled pseudo still lifes in Conway's Game of Life, up to rotation and reflection)". OEIS Foundation. https://oeis.org/A056613.
- ↑ Sloane, N. J. A., ed. "Sequence A068140 (Smaller of two consecutive numbers each divisible by a cube greater than one)". OEIS Foundation. https://oeis.org/A068140.
- ↑ Sloane, N. J. A., ed. "Sequence A030272 (Number of partitions of n^3 into distinct cubes)". OEIS Foundation. https://oeis.org/A030272.
- ↑ Sloane, N. J. A., ed. "Sequence A018818 (Number of partitions of n into divisors of n)". OEIS Foundation. https://oeis.org/A018818.
- ↑ Sloane, N. J. A., ed. "Sequence A071401 (Rounded volume of a regular dodecahedron with edge length n)". OEIS Foundation. https://oeis.org/A071401.
- ↑
^{293.0}^{293.1}^{293.2}"Sloane's A002407 : Cuban primes". OEIS Foundation. https://oeis.org/A002407. - ↑ Sloane, N. J. A., ed. "Sequence A059802 (Numbers k such that 5^k - 4^k is prime)". OEIS Foundation. https://oeis.org/A059802.
- ↑
^{295.0}^{295.1}Sloane, N. J. A., ed. "Sequence A082982 (Numbers k such that k, k+1 and k+2 are sums of 2 squares)". OEIS Foundation. https://oeis.org/A082982. - ↑ Sloane, N. J. A., ed. "Sequence A057562 (Number of partitions of n into parts all relatively prime to n)". OEIS Foundation. https://oeis.org/A057562.
- ↑ Sloane, N. J. A., ed. "Sequence A000230 (smallest prime p such that there is a gap of exactly 2n between p and next prime)". OEIS Foundation. https://oeis.org/A000230.
- ↑ Sloane, N. J. A., ed. "Sequence A261983 (Number of compositions of n such that at least two adjacent parts are equal)". OEIS Foundation. https://oeis.org/A261983.
- ↑ Sloane, N. J. A., ed. "Sequence A053781 (Numbers k that divide the sum of the first k composite numbers)". OEIS Foundation. https://oeis.org/A053781.
- ↑ Sloane, N. J. A., ed. "Sequence A140480 (RMS numbers: numbers n such that root mean square of divisors of n is an integer)". OEIS Foundation. https://oeis.org/A140480.
- ↑ Sloane, N. J. A., ed. "Sequence A023108 (Positive integers which apparently never result in a palindrome under repeated applications of the function A056964(x))". OEIS Foundation. https://oeis.org/A023108.
- ↑ Sloane, N. J. A., ed. "Sequence A098859 (Number of partitions of n into parts each of which is used a different number of times)". OEIS Foundation. https://oeis.org/A098859.
- ↑ Sloane, N. J. A., ed. "Sequence A286518 (Number of finite connected sets of positive integers greater than one with least common multiple n)". OEIS Foundation. https://oeis.org/A286518.
- ↑ Sloane, N. J. A., ed. "Sequence A004041 (Scaled sums of odd reciprocals: (2*n + 1)!!*(Sum_{0..n} 1/(2*k + 1)))". OEIS Foundation. https://oeis.org/A004041.
- ↑ {{cite OEIS<A023359|Number of compositions (ordered partitions) of n into powers of 2}}
- ↑ Sloane, N. J. A., ed. "Sequence A000787 (Strobogrammatic numbers: the same upside down)". OEIS Foundation. https://oeis.org/A000787.
- ↑ Sloane, N. J. A., ed. "Sequence A224930 (Numbers n such that n divides the concatenation of all divisors in descending order)". OEIS Foundation. https://oeis.org/A224930.
- ↑ Sloane, N. J. A., ed. "Sequence A294286 (Sum of the squares of the parts in the partitions of n into two distinct parts)". OEIS Foundation. https://oeis.org/A294286.
- ↑ "Sloane's A000073 : Tribonacci numbers". OEIS Foundation. https://oeis.org/A000073.
- ↑ Sloane, N. J. A., ed. "Sequence A020989 ((5*4^n - 2)/3)". OEIS Foundation. https://oeis.org/A020989.
- ↑ Sloane, N. J. A., ed. "Sequence A331378 (Numbers whose product of prime indices is divisible by their sum of prime factors)". OEIS Foundation. https://oeis.org/A331378.
- ↑ Sloane, N. J. A., ed. "Sequence A301700 (Number of aperiodic rooted trees with n nodes)". OEIS Foundation. https://oeis.org/A301700.
- ↑ Sloane, N. J. A., ed. "Sequence A331452 (number of regions (or cells) formed by drawing the line segments connecting any two of the 2*(m+n) perimeter points of an m X n grid of squares)". OEIS Foundation. https://oeis.org/A331452.
- ↑ Sloane, N. J. A., ed. "Sequence A056045 ("Sum_{d divides n}(binomial(n,d))")". OEIS Foundation. https://oeis.org/A056045.
- ↑ "Sloane's A007850 : Giuga numbers". OEIS Foundation. https://oeis.org/A007850.
- ↑ Sloane, N. J. A., ed. "Sequence A161757 ((prime(n))^2 - (nonprime(n))^2)". OEIS Foundation. https://oeis.org/A161757.
- ↑ Sloane, N. J. A., ed. "Sequence A078374 (Number of partitions of n into distinct and relatively prime parts)". OEIS Foundation. https://oeis.org/A078374.
- ↑ Sloane, N. J. A., ed. "Sequence A167008 (Sum_{0..n} C(n,k)^k)". OEIS Foundation. https://oeis.org/A167008.
- ↑ Sloane, N. J. A., ed. "Sequence A033581 (6*n^2)". OEIS Foundation. https://oeis.org/A033581.
- ↑ Sloane, N. J. A., ed. "Sequence A036469 (Partial sums of A000009 (partitions into distinct parts))". OEIS Foundation. https://oeis.org/A036469.
- ↑ Sloane, N. J. A., ed. "Sequence A350507 (Number of (not necessarily connected) unit-distance graphs on n nodes)". OEIS Foundation. https://oeis.org/A350507.
- ↑ Sloane, N. J. A., ed. "Sequence A102627 (Number of partitions of n into distinct parts in which the number of parts divides n)". OEIS Foundation. https://oeis.org/A102627.
- ↑ Sloane, N. J. A., ed. "Sequence A216955 (number of binary sequences of length n and curling number k)". OEIS Foundation. https://oeis.org/A216955.
- ↑ Sloane, N. J. A., ed. "Sequence A001523 (Number of stacks, or planar partitions of n; also weakly unimodal compositions of n)". OEIS Foundation. https://oeis.org/A001523.
- ↑ Sloane, N. J. A., ed. "Sequence A065764 (Sum of divisors of square numbers)". OEIS Foundation. https://oeis.org/A065764.
- ↑ Sloane, N. J. A., ed. "Sequence A220881 (Number of nonequivalent dissections of an n-gon into n-3 polygons by nonintersecting diagonals up to rotation)". OEIS Foundation. https://oeis.org/A220881.
- ↑ Sloane, N. J. A., ed. "Sequence A154964 (3*a(n-1) + 6*a(n-2))". OEIS Foundation. https://oeis.org/A154964.
- ↑ Sloane, N. J. A., ed. "Sequence A055327 (Triangle of rooted identity trees with n nodes and k leaves)". OEIS Foundation. https://oeis.org/A055327.
- ↑ Sloane, N. J. A., ed. "Sequence A316322 (Sum of piles of first n primes)". OEIS Foundation. https://oeis.org/A316322.
- ↑ Sloane, N. J. A., ed. "Sequence A045944 (Rhombic matchstick numbers: n*(3*n+2))". OEIS Foundation. https://oeis.org/A045944.
- ↑ Sloane, N. J. A., ed. "Sequence A127816 (least k such that the remainder when 6^k is divided by k is n)". OEIS Foundation. https://oeis.org/A127816.
- ↑ Sloane, N. J. A., ed. "Sequence A005317 ((2^n + C(2*n,n))/2)". OEIS Foundation. https://oeis.org/A005317.
- ↑ Sloane, N. J. A., ed. "Sequence A064118 (Numbers k such that the first k digits of e form a prime)". OEIS Foundation. https://oeis.org/A064118.
- ↑ Sloane, N. J. A., ed. "Sequence A325860 (Number of subsets of {1..n} such that every pair of distinct elements has a different quotient)". OEIS Foundation. https://oeis.org/A325860.
- ↑ Sloane, N. J. A., ed. "Sequence A073592 (Euler transform of negative integers)". OEIS Foundation. https://oeis.org/A073592.
- ↑ Sloane, N. J. A., ed. "Sequence A025047 (Alternating compositions, i.e., compositions with alternating increases and decreases, starting with either an increase or a decrease)". OEIS Foundation. https://oeis.org/A025047.
- ↑ Sloane, N. J. A., ed. "Sequence A288253 (Number of heptagons that can be formed with perimeter n)". OEIS Foundation. https://oeis.org/A288253.
- ↑ Sloane, N. J. A., ed. "Sequence A235488 (Squarefree numbers which yield zero when their prime factors are xored together)". OEIS Foundation. https://oeis.org/A235488.
- ↑ Sloane, N. J. A., ed. "Sequence A075213 (Number of polyhexes with n cells that tile the plane isohedrally but not by translation or by 180-degree rotation (Conway criterion))". OEIS Foundation. https://oeis.org/A075213.
- ↑ "Sloane's A054377 : Primary pseudoperfect numbers". OEIS Foundation. https://oeis.org/A054377.
- ↑ Kellner, Bernard C.; 'The equation denom(B
_{n}) =*n*has only one solution' - ↑ Sloane, N. J. A., ed. "Sequence A006318 (Large Schröder numbers)". OEIS Foundation. https://oeis.org/A006318. Retrieved 2016-05-22.
- ↑ "Sloane's A000058 : Sylvester's sequence". OEIS Foundation. https://oeis.org/A000058.
- ↑ Sloane, N. J. A., ed. "Sequence A083186 (Sum of first n primes whose indices are primes)". OEIS Foundation. https://oeis.org/A083186.
- ↑ Sloane, N. J. A., ed. "Sequence A005260 (Sum_{0..n} binomial(n,k)^4)". OEIS Foundation. https://oeis.org/A005260.
- ↑ Sloane, N. J. A., ed. "Sequence A056877 (Number of polyominoes with n cells, symmetric about two orthogonal axes)". OEIS Foundation. https://oeis.org/A056877.
- ↑ Sloane, N. J. A., ed. "Sequence A061801 ((7*6^n - 2)/5)". OEIS Foundation. https://oeis.org/A061801.
- ↑ Sloane, N. J. A., ed. "Sequence A152927 (Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of k 4-gonal polygonal components chained with string components of length 1 as k varies)". OEIS Foundation. https://oeis.org/A152927.
- ↑ Sloane, N. J. A., ed. "Sequence A037032 (Total number of prime parts in all partitions of n)". OEIS Foundation. https://oeis.org/A037032.
- ↑ Sloane, N. J. A., ed. "Sequence A101301 (The sum of the first n primes, minus n)". OEIS Foundation. https://oeis.org/A101301.
- ↑ Sloane, N. J. A., ed. "Sequence A332835 (Number of compositions of n whose run-lengths are either weakly increasing or weakly decreasing)". OEIS Foundation. https://oeis.org/A332835. Retrieved 2022-06-02.
- ↑ Sloane, N. J. A., ed. "Sequence A000230 (smallest prime p such that there is a gap of exactly 2n between p and next prime, or -1 if no such prime exists)". OEIS Foundation. https://oeis.org/A000230.
- ↑ Sloane, N. J. A., ed. "Sequence A004068 (Number of atoms in a decahedron with n shells)". OEIS Foundation. https://oeis.org/A004068.
- ↑ Sloane, N. J. A., ed. "Sequence A001905 (From higher-order Bernoulli numbers: absolute value of numerator of D-number D2n(2n-1))". OEIS Foundation. https://oeis.org/A001905.
- ↑ Sloane, N. J. A., ed. "Sequence A214083 (floor(n!^(1/3)))". OEIS Foundation. https://oeis.org/A214083.
- ↑ Sloane, N. J. A., ed. "Sequence A000081 (Number of unlabeled rooted trees with n nodes (or connected functions with a fixed point))". OEIS Foundation. https://oeis.org/A000081.
- ↑ Sloane, N. J. A., ed. "Sequence A354493 (Number of quantales on n elements, up to isomorphism)". OEIS Foundation. https://oeis.org/A354493.
- ↑ Sloane, N. J. A., ed. "Sequence A000240 (Rencontres numbers: number of permutations of [n with exactly one fixed point)"]. OEIS Foundation. https://oeis.org/A000240.
- ↑ Sloane, N. J. A., ed. "Sequence A000602 (Number of n-node unrooted quartic trees; number of n-carbon alkanes C(n)H(2n+2) ignoring stereoisomers)". OEIS Foundation. https://oeis.org/A000602.
- ↑ ""Aztec Diamond"". https://mathworld.wolfram.com/AztecDiamond.html.
- ↑ Sloane, N. J. A., ed. "Sequence A082671 (Numbers n such that (n!-2)/2 is a prime)". OEIS Foundation. https://oeis.org/A082671.
- ↑ Sloane, N. J. A., ed. "Sequence A023811 (Largest metadrome (number with digits in strict ascending order) in base n)". OEIS Foundation. https://oeis.org/A023811.
- ↑ Sloane, N. J. A., ed. "Sequence A000990 (Number of plane partitions of n with at most two rows)". OEIS Foundation. https://oeis.org/A000990.
- ↑ Sloane, N. J. A., ed. "Sequence A164652 (Hultman numbers)". OEIS Foundation. https://oeis.org/A164652.
- ↑ Sloane, N. J. A., ed. "Sequence A007530 (Prime quadruples: numbers k such that k, k+2, k+6, k+8 are all prime)". OEIS Foundation. https://oeis.org/A007530.
- ↑ Sloane, N. J. A., ed. "Sequence A057568 (Number of partitions of n where n divides the product of the parts)". OEIS Foundation. https://oeis.org/A057568.
- ↑ Sloane, N. J. A., ed. "Sequence A011757 (prime(n^2))". OEIS Foundation. https://oeis.org/A011757.
- ↑ Sloane, N. J. A., ed. "Sequence A004799 (Self convolution of Lucas numbers)". OEIS Foundation. https://oeis.org/A004799.
- ↑ Sloane, N. J. A., ed. "Sequence A005920 (Tricapped prism numbers)". OEIS Foundation. https://oeis.org/A005920.
- ↑ Sloane, N. J. A., ed. "Sequence A000609 (Number of threshold functions of n or fewer variables)". OEIS Foundation. https://oeis.org/A000609.
- ↑ Sloane, N. J. A., ed. "Sequence A259793 (Number of partitions of n^4 into fourth powers)". OEIS Foundation. https://oeis.org/A259793.
- ↑ Sloane, N. J. A., ed. "Sequence A006785 (Number of triangle-free graphs on n vertices)". OEIS Foundation. https://oeis.org/A006785.
- ↑ Sloane, N. J. A., ed. "Sequence A002998 (Smallest multiple of n whose digits sum to n)". OEIS Foundation. https://oeis.org/A002998.
- ↑ Sloane, N. J. A., ed. "Sequence A005987 (Number of symmetric plane partitions of n)". OEIS Foundation. https://oeis.org/A005987.
- ↑ Sloane, N. J. A., ed. "Sequence A023431 (Generalized Catalan Numbers)". OEIS Foundation. https://oeis.org/A023431.
- ↑ Sloane, N. J. A., ed. "Sequence A217135 (Numbers n such that 3^n - 8 is prime)". OEIS Foundation. https://oeis.org/A217135.
- ↑ "Sloane's A034897 : Hyperperfect numbers". OEIS Foundation. https://oeis.org/A034897.
- ↑ Sloane, N. J. A., ed. "Sequence A240736 (Number of compositions of n having exactly one fixed point)". OEIS Foundation. https://oeis.org/A240736.
- ↑ Sloane, N. J. A., ed. "Sequence A007070 (4*a(n-1) - 2*a(n-2))". OEIS Foundation. https://oeis.org/A007070.
- ↑ Sloane, N. J. A., ed. "Sequence A000412 (Number of bipartite partitions of n white objects and 3 black ones)". OEIS Foundation. https://oeis.org/A000412.
- ↑ Sloane, N. J. A., ed. "Sequence A027851 (Number of nonisomorphic semigroups of order n)". OEIS Foundation. https://oeis.org/A027851.
- ↑ Sloane, N. J. A., ed. "Sequence A003060 (Smallest number with reciprocal of period length n in decimal (base 10))". OEIS Foundation. https://oeis.org/A003060.
- ↑ Sloane, N. J. A., ed. "Sequence A008514 (4-dimensional centered cube numbers)". OEIS Foundation. https://oeis.org/A008514.
- ↑ Sloane, N. J. A., ed. "Sequence A024012 (2^n - n^2)". OEIS Foundation. https://oeis.org/A024012.
- ↑ Sloane, N. J. A., ed. "Sequence A002845 (Number of distinct values taken by 2^2^...^2 (with n 2's and parentheses inserted in all possible ways))". OEIS Foundation. https://oeis.org/A002845.
- ↑ "Sloane's A051870 : 18-gonal numbers". OEIS Foundation. https://oeis.org/A051870.
- ↑ Sloane, N. J. A., ed. "Sequence A045648 (Number of chiral n-ominoes in (n-1)-space, one cell labeled)". OEIS Foundation. https://oeis.org/A045648.
- ↑ Sloane, N. J. A., ed. "Sequence A000127 (Maximal number of regions obtained by joining n points around a circle by straight lines. Also number of regions in 4-space formed by n-1 hyperplanes)". OEIS Foundation. https://oeis.org/A000127.
- ↑ Sloane, N. J. A., ed. "Sequence A178084 (Numbers k for which 10k + 1, 10k + 3, 10k + 7, 10k + 9 and 10k + 13 are primes)". OEIS Foundation. https://oeis.org/A178084.
- ↑
^{390.0}^{390.1}Sloane, N. J. A., ed. "Sequence A007419 (Largest number not the sum of distinct n-th-order polygonal numbers)". OEIS Foundation. https://oeis.org/A007419. - ↑ Sloane, N. J. A., ed. "Sequence A100953 (Number of partitions of n into relatively prime parts such that multiplicities of parts are also relatively prime)". OEIS Foundation. https://oeis.org/A100953.
- ↑ Sloane, N. J. A., ed. "Sequence A226366 (Numbers k such that 5*2^k + 1 is a prime factor of a Fermat number 2^(2^m) + 1 for some m)". OEIS Foundation. https://oeis.org/A226366.
- ↑ Sloane, N. J. A., ed. "Sequence A319014 (1*2*3 + 4*5*6 + 7*8*9 + 10*11*12 + 13*14*15 + 16*17*18 + ... + (up to n))". OEIS Foundation. https://oeis.org/A319014.
- ↑ Sloane, N. J. A., ed. "Sequence A055621 (Number of covers of an unlabeled n-set)". OEIS Foundation. https://oeis.org/A055621.
- ↑ Sloane, N. J. A., ed. "Sequence A000522 (Total number of ordered k-tuples of distinct elements from an n-element set)". OEIS Foundation. https://oeis.org/A000522.
- ↑ Sloane, N. J. A., ed. "Sequence A104621 (Heptanacci-Lucas numbers)". OEIS Foundation. https://oeis.org/A104621.
- ↑ Sloane, N. J. A., ed. "Sequence A005449 (Second pentagonal numbers)". OEIS Foundation. https://oeis.org/A005449.
- ↑ Sloane, N. J. A., ed. "Sequence A002982 (Numbers n such that n! - 1 is prime)". OEIS Foundation. https://oeis.org/A002982.
- ↑ Sloane, N. J. A., ed. "Sequence A030238 (Backwards shallow diagonal sums of Catalan triangle A009766)". OEIS Foundation. https://oeis.org/A030238.
- ↑ Sloane, N. J. A., ed. "Sequence A089046 (Least edge-length of a square dissectable into at least n squares in the Mrs. Perkins's quilt problem)". OEIS Foundation. https://oeis.org/A089046.
- ↑ Sloane, N. J. A., ed. "Sequence A065900 (Numbers n such that sigma(n) equals sigma(n-1) + sigma(n-2))". OEIS Foundation. https://oeis.org/A065900.
- ↑ Jon Froemke; Jerrold W. Grossman (Feb 1993). "A Mod-n Ackermann Function, or What's So Special About 1969?".
*The American Mathematical Monthly*(Mathematical Association of America)**100**(2): 180–183. doi:10.2307/2323780. https://archive.org/details/sim_american-mathematical-monthly_1993-02_100_2/page/180. - ↑ Sloane, N. J. A., ed. "Sequence A052542 (2*a(n-1) + a(n-2))". OEIS Foundation. https://oeis.org/A052542.
- ↑ Sloane, N. J. A., ed. "Sequence A024069 (6^n - n^7)". OEIS Foundation. https://oeis.org/A024069.
- ↑ Sloane, N. J. A., ed. "Sequence A217076 (Numbers n such that (n^37-1)/(n-1) is prime)". OEIS Foundation. https://oeis.org/A217076.
- ↑ Sloane, N. J. A., ed. "Sequence A302545 (Number of non-isomorphic multiset partitions of weight n with no singletons)". OEIS Foundation. https://oeis.org/A302545.
- ↑ Sloane, N. J. A., ed. "Sequence A277288 (Positive integers n such that n divides (3^n + 5))". OEIS Foundation. https://oeis.org/A277288.
- ↑ Sloane, N. J. A., ed. "Sequence A187220 (Gullwing sequence)". OEIS Foundation. https://oeis.org/A187220.
- ↑ Sloane, N. J. A., ed. "Sequence A046351 (Palindromic composite numbers with only palindromic prime factors)". OEIS Foundation. https://oeis.org/A046351.
- ↑ Sloane, N. J. A., ed. "Sequence A000612 (Number of P-equivalence classes of switching functions of n or fewer variables, divided by 2)". OEIS Foundation. https://oeis.org/A000612.
- ↑ OEIS: A059801
- ↑ Sloane, N. J. A., ed. "Sequence A002470 (Glaisher's function W(n))". OEIS Foundation. https://oeis.org/A002470.
- ↑ Sloane, N. J. A., ed. "Sequence A263341 (Triangle read by rows: T(n,k) is the number of unlabeled graphs on n vertices with independence number k)". OEIS Foundation. https://oeis.org/A263341.
- ↑ Sloane, N. J. A., ed. "Sequence A089085 (Numbers k such that (k! + 3)/3 is prime)". OEIS Foundation. https://oeis.org/A089085.
- ↑ Sloane, N. J. A., ed. "Sequence A011755 (Sum_{1..n} k*phi(k))". OEIS Foundation. https://oeis.org/A011755.
- ↑ Sloane, N. J. A., ed. "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". OEIS Foundation. https://oeis.org/A005448.,
- ↑ Sloane, N. J. A., ed. "Sequence A038823 (Number of primes between n*1000 and (n+1)*1000)". OEIS Foundation. https://oeis.org/A038823.
- ↑ Stein, William A. (10 February 2017). "The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture". https://wstein.org/talks/2017-02-10-wing-rh_and_bsd/.

Original source: https://en.wikipedia.org/wiki/1000 (number).
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