View source for List of OEIS sequences

This article provides a list of [[Integer sequence|integer sequence]]s in the [[On-Line Encyclopedia of Integer Sequences]] that have their own English Wikipedia entries.
{|class="wikitable sortable"
! OEIS link !! Name !! First elements !! Short description
|-
| {{OEIS link|A000002}} || [[Kolakoski sequence]] || {1, 2, 2, 1, 1, 2, 1, 2, 2, 1, ...}
| The {{math|''n''}}th term describes the length of the {{math|''n''}}th run
|-
| {{OEIS link|A000010}} || [[Euler's totient function]] {{math|''φ''(''n'')}} || {1, 1, 2, 2, 4,  2,  6, 4, 6, 4, ...}  
| {{math|''φ''(''n'')}} is the number of positive integers not greater than {{math|''n''}} that are prime to {{math|''n''}}.  
|-
| {{OEIS link|A000027}} || [[Natural number]]s || {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...} 
| The natural numbers (positive integers) {{math|''n'' ∈ ℕ}}.
|-
| {{OEIS link|A000032}} || [[Lucas number]]s {{math|''L''(''n'')}} || {2, 1, 3, 4, 7, 11, 18, 29, 47, 76, ...}  
| {{math|''L''(''n'') {{=}} ''L''(''n'' &minus; 1) + ''L''(''n'' &minus; 2)}} for {{math|''n'' &ge; 2}}, with {{math|''L''(0) {{=}} 2}} and {{math|''L''(1) {{=}} 1}}.
|-
| {{OEIS link|A000040}} || [[Prime number]]s {{math|''p''<sub>''n''</sub>}} || {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...} 
| The prime numbers {{math|''p''<sub>''n''</sub>}}, with {{math|''n'' &ge; 1}}.
|-
| {{OEIS link|A000041}} || Partition numbers <br>{{math|''P''<sub>''n''</sub>}} || {1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, ...}
| The partition numbers, number of additive breakdowns of n.
|-
| {{OEIS link|A000043}} || [[Mersenne prime]] exponents || {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, ...}
| Primes {{math|''p''}} such that {{math|2<sup>''p''</sup> &minus; 1}} is prime.
|-
| {{OEIS link|A000045}} || [[Fibonacci number]]s {{math|''F''(''n'')}} || {0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...}  
| {{math|''F''(''n'') {{=}} ''F''(''n'' &minus; 1) + ''F''(''n'' &minus; 2)}} for {{math|''n'' &ge; 2}}, with {{math|''F''(0) {{=}} 0}} and {{math|''F''(1) {{=}} 1}}.
|-
| {{OEIS link|A000058}} || [[Sylvester's sequence]] || {2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443, ...}  
| {{math|''a''(''n'' + 1) {{=}} ''a''(''n'')&sdot;''a''(''n'' &minus; 1)&sdot; ⋯ &sdot;''a''(0) + 1 {{=}} ''a''(''n'')<sup>2</sup> &minus; ''a''(''n'') + 1}} for {{math|''n'' &ge; 1}}, with {{math|''a''(0) {{=}} 2}}.
|-
| {{OEIS link|A000073}} || Tribonacci numbers || {0, 1, 1, 2, 4, 7, 13, 24, 44, 81, ...}  
| {{math|''T''(''n'') {{=}} ''T''(''n'' &minus; 1) + ''T''(''n'' &minus; 2) + ''T''(''n'' &minus; 3)}} for {{math|''n'' &ge; 3}}, with <!--
-->{{math|''T''(0) {{=}} 0 and ''T''(1) {{=}} ''T''(2) {{=}} 1}}.
|-
| {{OEIS link|A000105}} || Polyominoes || {1, 1, 1, 2, 5, 12, 35, 108, 369, ...}  
| The number of free polyominoes with {{math|''n''}} cells.
|-
| {{OEIS link|A000108}} || [[Catalan number]]s {{math|''C''<sub>''n''</sub>}} || {1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, ...}  
| <math>C_n = \frac{1}{n+1}{2n\choose n} = \frac{(2n)!}{(n+1)!\,n!} = \prod\limits_{k=2}^{n}\frac{n+k}{k},\quad n \ge 0.</math>
|-
| {{OEIS link|A000110}} || [[Bell number]]s {{math|''B''<sub>''n''</sub>}} || {1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, ...}  
| {{math|''B''<sub>''n''</sub>}} is the number of partitions of a set with {{math|''n''}} elements.
|-
| {{OEIS link|A000111}} || Euler zigzag numbers {{math|''E''<sub>''n''</sub>}} || {1, 1, 1, 2, 5, 16, 61, 272, 1385, 7936, ...} 
| {{math|''E''<sub>''n''</sub>}} is the number of linear extensions of the "zig-zag" poset.
|-
| {{OEIS link|A000124}} || [[Lazy caterer's sequence]] || {1, 2, 4, 7, 11, 16, 22, 29, 37, 46, ...}  
| The maximal number of pieces formed when slicing a pancake with {{math|''n''}} cuts.
|-
| {{OEIS link|A000129}} || [[Pell number]]s {{math|''P''<sub>''n''</sub>}} || {0, 1, 2, 5, 12, 29, 70, 169, 408, 985, ...}  
| {{math|''a''(''n'') {{=}} 2''a''(''n'' &minus; 1) + ''a''(''n'' &minus; 2)}} for {{math|''n'' &ge; 2}}, with {{math|''a''(0) {{=}} 0, ''a''(1) {{=}} 1}}.
|-
| {{OEIS link|A000142}} || [[Factorial]]s {{math|''n''!}} || {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, ...}  
| {{math|''n''! :{{=}} 1&sdot;2&sdot;3&sdot;4&sdot; ⋯ &sdot;''n''}} for {{math|''n'' &ge; 1}}, with {{math|0! {{=}} 1}} (empty product).
|-
| {{OEIS link|A000166}} || [[Derangement]]s || {1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, 14684570, 176214841, ...}  
| Number of permutations of n elements with no fixed points.
|-
| {{OEIS link|A000203}} || [[Divisor function]] {{math|''&sigma;''(''n'')}} || {1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, ...} 
| {{math|''&sigma;''(''n'') :{{=}} ''&sigma;''<sub>1</sub>(''n'')}} is the sum of divisors of a positive integer {{math|''n''}}.
|-
| {{OEIS link|A000215}} || [[Fermat number]]s {{math|''F''<sub>''n''</sub>}} || {3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, 340282366920938463463374607431768211457, ...}  
| {{math|''F''<sub>''n''</sub> {{=}} ''2''<sup>''2''<sup>''n''</sup></sup> + 1}} for {{math|''n'' &ge; 0}}.
|-
| {{OEIS link|A000217}} || [[Triangular number]]s {{math|''t''(''n'')}} || {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, ...}  
| {{math|''t''(''n'') {{=}} ''C''(''n'' + 1, 2) {{=}} {{sfrac|''n'' (''n'' + 1)|2}} {{=}} 1 + 2 + ⋯ + ''n''}} for {{math|''n'' &ge; 1}}, with {{math|''t''(0) {{=}} 0}} (empty sum).
|-
| {{OEIS link|A000238}} || [[Polytree]]s || {1, 1, 3, 8, 27, 91, 350, 1376, 5743, 24635, 108968, ...}
| Number of oriented trees with n nodes.
|-
| {{OEIS link|A000290}} || [[Square (algebra)|Square number]]s {{math|''n''<sup>2</sup>}} || {0, 1, 4, 9, 16, 25, 36, 49, 64, 81, ...}
| {{math|''n''<sup>2</sup> {{=}} ''n'' × ''n''}}
|-
| {{OEIS link|A000292}} || Tetrahedral numbers {{math|''T''(''n'')}} || {0, 1, 4, 10, 20, 35, 56, 84, 120, 165, ...}  
| {{math|''T''(''n'')}} is the sum of the first {{math|''n''}} triangular numbers, with {{math|''T''(0) {{=}} 0}} (empty sum).
|-
| {{OEIS link|A000330}} || Square pyramidal numbers || {0, 1, 5, 14, 30, 55, 91, 140, 204, 285, ...}  
| {{math| {{sfrac|''n'' (''n'' + 1)(2''n'' + 1)|6}} }}: The number of stacked spheres in a pyramid with a square base.
|-
| {{OEIS link|A000396}} || [[Perfect number]]s || {6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128, ...} 
| {{math|''n''}} is equal to the sum {{math|''s''(''n'') {{=}} ''&sigma;''(''n'') &minus; ''n''}} of the proper divisors of {{math|''n''}}.
|-
| {{OEIS link|A000578}} || [[Cube (algebra)|Cube number]]s {{math|''n''<sup>3</sup>}} || {0, 1, 8, 27, 64, 125, 216, 343, 512, 729, ...}
| {{math|''n''<sup>3</sup> {{=}} ''n'' × ''n'' × ''n''}}
|-
| {{OEIS link|A000584}} || [[Fifth power (algebra)|Fifth power]]s || {0, 1, 32, 243, 1024, 3125, 7776, 16807, 32768, 59049, 100000, ...}
| {{math|size=120%|1=''n''<sup>5</sup>}}
|-
| {{OEIS link|A000668}} || [[Mersenne prime]]s || {3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, ...}  || {{math|2<sup>''p''</sup> &minus; 1}} is prime, where {{math|''p''}} is a prime. 
|-
| {{OEIS link|A000793}} || [[Landau's function]] || {1, 1, 2, 3, 4, 6, 6, 12, 15, 20, ...}  
| The largest order of permutation of {{math|''n''}} elements.
|-
| {{OEIS link|A000796}} || Decimal expansion of [[Pi|{{math|''&pi;''}}]] || {3, 1, 4, 1, 5, 9, 2, 6, 5, 3, ...} 
|  Ratio of a circle's circumference to its diameter.
|-
| {{OEIS link|A000930}} || Narayana's cows || {1, 1, 1, 2, 3, 4, 6, 9, 13, 19, ...}
| The number of cows each year if each cow has one cow a year beginning its fourth year.
|-
| {{OEIS link|A000931}} || [[Padovan sequence]] || {1, 1, 1, 2, 2, 3, 4, 5, 7, 9, ...}  
| {{math|''P''(''n'') {{=}} ''P''(''n'' &minus; 2) + ''P''(''n'' &minus; 3)}} for {{math|''n'' &ge; 3}}, with {{math|''P''(0) {{=}} ''P''(1) {{=}} ''P''(2) {{=}} 1}}.
|-
| {{OEIS link|A000945}} || [[Euclid–Mullin sequence]] || {2, 3, 7, 43, 13, 53, 5, 6221671, 38709183810571, 139, ...}  
| {{math|''a''(1) {{=}} 2; ''a''(''n'' + 1)}} is smallest prime factor of {{math|''a''(1) ''a''(2)'' ⋯ a''(''n'') + 1}}.
|-
| {{OEIS link|A000959}} || [[Lucky number]]s || {1, 3, 7, 9, 13, 15, 21, 25, 31, 33, ...} 
| A natural number in a set that is filtered by a sieve.
|-
| {{OEIS link|A001006}} || [[Motzkin number]]s || {1, 1, 2, 4, 9, 21, 51, 127, 323, 835, ...}  
| The number of ways of drawing any number of nonintersecting chords joining {{math|''n''}} (labeled) points on a circle.
|-
| {{OEIS link|A001045}} || [[Jacobsthal number]]s || {0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, ...} 
| {{math|''a''(''n'') {{=}} ''a''(''n'' &minus; 1) + 2''a''(''n'' &minus; 2)}} for {{math|''n'' &ge; 2}}, with {{math|''a''(0) {{=}} 0, ''a''(1) {{=}} 1}}.
|-
| {{OEIS link|A001065}} || Sum of proper divisors {{math|''s''(''n'')}} || {0, 1, 1, 3, 1,  6, 1, 7, 4, 8, ...} 
| {{math|''s''(''n'') {{=}} ''&sigma;''(''n'') &minus; ''n''}} is the sum of the proper divisors of the positive integer {{math|''n''}}. 
|-
| {{OEIS link|A001113}} || Decimal expansion of [[E (mathematical constant)|{{math|''e''}}]] || {2, 7, 1, 8, 2, 8, 1, 8, 2, 8, ...} 
| Euler's number in base 10. 
|-
| {{OEIS link|A001190}} || [[Wedderburn–Etherington number]]s || {0, 1, 1, 1, 2, 3, 6, 11, 23, 46, ...} 
| The number of binary rooted trees (every node has out-degree 0 or 2) with {{math|''n''}} endpoints (and {{math|2''n'' &minus; 1}} nodes in all).
|-
| {{OEIS link|A001220}} || [[Wieferich prime]]s || {1093, 3511}
|| Primes <math>p</math> satisfying {{math|2<sup>''p''-1</sup> ≡ 1 (mod ''p''<sup>2</sup>)}}. 
|-
| {{OEIS link|A001263}} || [[Narayana number]]s || {1, 1, 1, 1, 3, 1, 1, 6, 6, 1, 1, 10, 20, 10, 1, ...}
| <math>{1\over k}{n-1\choose k-1}{n\choose k-1}</math> read by rows.
|-
| {{OEIS link|A001316}} || [[Gould's sequence]] || {1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, ...}
| Number of odd entries in row n of Pascal's triangle.
|-
| {{OEIS link|A001358}} || [[Semiprime]]s || {4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ...}
| Products of two primes, not necessarily distinct.
|-
| {{OEIS link|A001462}} || [[Golomb sequence]] || {1, 2, 2, 3, 3, 4, 4, 4, 5, 5, ...} 
| {{math|''a''(''n'')}} is the number of times {{math|''n''}} occurs, starting with {{math|''a''(1) {{=}} 1}}.
|-
| {{OEIS link|A001608}} || [[Perrin number]]s {{math|''P''<sub>''n''</sub>}} || {3, 0, 2, 3, 2, 5, 5, 7, 10, 12, ...} 
| {{math|''P''(''n'') {{=}} ''P''(''n''−2) + ''P''(''n''−3)}} for {{math|''n'' &ge; 3}}, with {{math|''P''(0) {{=}} 3, ''P''(1) {{=}} 0, ''P''(2) {{=}} 2}}.
|-
| {{OEIS link|A001620}} || [[Euler–Mascheroni constant]] {{math|''&gamma;''}} || {5, 7, 7, 2, 1, 5, 6, 6, 4, 9, ...} 
| <math>\gamma = \lim_{n \rightarrow \infty } \left( \sum_{k=1}^n \frac{1}{k} - \ln(n) \right)=\lim_{b \rightarrow \infty } \int_1^b\left({1\over\lfloor x\rfloor}-{1\over x}\right)\,dx.</math>
|-
| {{OEIS link|A001622}} || Decimal expansion of the [[Golden ratio|golden ratio]] {{math|''&phi;''}} || {1, 6, 1, 8, 0, 3, 3, 9, 8, 8, ...} 
| {{math|''&phi;'' {{=}} {{sfrac|1 + {{sqrt|5}}|2}} {{=}} 1.6180339887...}} in base 10.
|-
| {{OEIS link|A001855}} || [[Sorting number]] || {0, 1, 3, 5, 8, 11, 14, 17, 21, 25, 29, 33, 37, 41, 45, 49 ...} 
|Used in the analysis of [[Comparison sort|comparison sort]]s.
|-
| {{OEIS link|A002064}} || [[Cullen number]]s {{math|''C''<sub>''n''</sub>}} || {1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153, 106497, ...} 
| {{math|''C''<sub>''n''</sub> {{=}} ''n''&sdot;2<sup>''n''</sup> + 1}}, with {{math|''n'' &ge; 0}}.
|-
| {{OEIS link|A002110}} || [[Primorial]]s {{math|''p''<sub>''n''</sub>#}} || {1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, ...} 
| {{math|''p''<sub>''n''</sub>#}}, the product of the first {{math|''n''}} primes.
|-
| {{OEIS link|A002113}} || [[Palindromic number]]s || {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...} 
| A number that remains the same when its digits are reversed.
|-
| {{OEIS link|A002182}} || [[Highly composite number]]s || {1, 2, 4, 6, 12, 24, 36, 48, 60, 120, ...} 
| A positive integer with more divisors than any smaller positive integer.
|-
| {{OEIS link|A002193}} || Decimal expansion of [[Square root of 2|{{math| {{sqrt|2}} }}]] || {1, 4, 1, 4, 2, 1, 3, 5, 6, 2, ...} 
| Square root of 2. 
|-
| {{OEIS link|A002201}} || [[Superior highly composite number]]s || {2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, ...} 
| A positive integer {{math|''n''}} for which there is an {{math|''e'' > 0}} such that {{math| {{sfrac|''d''(''n'')|''n''<sup>''e''</sup>}} &ge; {{sfrac|''d''(''k'')|''k''<sup>''e''</sup>}} }} for all {{math|''k'' > 1}}.
|-
| {{OEIS link|A002378}} || [[Pronic number]]s || {0, 2, 6, 12, 20, 30, 42, 56, 72, 90, ...} 
| {{math|2''t''(''n'') {{=}} ''n'' (''n'' + 1)}}, with {{math|''n'' &ge; 0}}.
|-
| {{OEIS link|A002559}} || [[Markov number]]s || {1, 2, 5, 13, 29, 34, 89, 169, 194, ...}
| Positive integer solutions of {{math|''x''<sup>2</sup> + ''y''<sup>2</sup> + ''z''<sup>2</sup> {{=}} 3''xyz''}}.
|-
| {{OEIS link|A002808}} || [[Composite number]]s || {4, 6, 8, 9, 10, 12, 14, 15, 16, 18, ...} 
| The numbers {{math|''n''}} of the form {{math|''xy''}} for {{math|''x'' > 1}} and {{math|''y'' > 1}}.
|-
| {{OEIS link|A002858}} || [[Ulam number]] || {1, 2, 3, 4, 6, 8, 11, 13, 16, 18, ...} 
| {{math|''a''(1) {{=}} 1; ''a''(2) {{=}} 2;}} for {{math|''n'' > 2, ''a''(''n'')}} is least number {{math| > ''a''(''n'' &minus; 1)}} which is a unique sum of two distinct earlier terms; semiperfect.
|-
| {{OEIS link|A002863}} || [[Prime knot]]s || {0, 0, 1, 1, 2, 3, 7, 21, 49, 165, 552, 2176, 9988, ...} 
| The number of prime knots with n crossings.
|-
| {{OEIS link|A002997}} || [[Carmichael number]]s || {561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341, ...} 
| Composite numbers {{math|''n''}} such that {{math|''a''<sup>''n'' &minus; 1</sup> ≡ 1 (mod ''n'')}} if {{math|''a''}} is prime to {{math|''n''}}.
|-
| {{OEIS link|A003154}} || Star numbers || {1, 13, 37, 73, 121, 181, 253, 337, 433, 541, 661, 793, 937, ...} 
| The ''n''th star number is ''S<sub>n</sub>'' = 6''n''(''n'' − 1) + 1.
|-
| {{OEIS link|A003261}} || [[Woodall number]]s || {1, 7, 23, 63, 159, 383, 895, 2047, 4607, ...} 
| {{math|''n''&sdot;2<sup>''n''</sup> &minus; 1}}, with {{math|''n'' &ge; 1}}.
|-
| {{OEIS link|A003459}} || [[Permutable prime]]s || {2, 3, 5, 7, 11, 13, 17, 31, 37, 71, ...} 
| The numbers for which every permutation of digits is a prime.
|-
| {{OEIS link|A003601}} || [[Arithmetic number]]s || {1, 3, 5, 6, 7, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 27, ...} 
| An integer for which the average of its positive divisors is also an integer.
|-
| {{OEIS link|A004490}} || [[Colossally abundant number]]s || {2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, ...} 
| A number ''n'' is colossally abundant iff there is an ε&nbsp;&gt;&nbsp;0 such that for all ''k''&nbsp;>&nbsp;1,

:<math>\frac{\sigma(n)}{n^{1+\varepsilon}}\geq\frac{\sigma(k)}{k^{1+\varepsilon}},</math>

where σ denotes the sum-of-divisors function.
|-
| {{OEIS link|A005044}} || [[Alcuin's sequence]] || {0, 0, 0, 1, 0, 1, 1, 2, 1, 3, 2, 4, 3, 5, 4, 7, 5, 8, 7, 10, 8, 12, 10, 14, ...} 
| Number of triangles with integer sides and perimeter {{math|''n''}}.
|-
| {{OEIS link|A005100}} || [[Deficient number]]s || {1, 2, 3, 4, 5, 7, 8, 9, 10, 11, ...} 
| Positive integers {{math|''n''}} such that {{math|''&sigma;''(''n'') < 2''n''}}.
|-
| {{OEIS link|A005101}} || [[Abundant number]]s || {12, 18, 20, 24, 30, 36, 40, 42, 48, 54, ...} 
| Positive integers {{math|''n''}} such that {{math|''&sigma;''(''n'') > 2''n''}}.
|-
| {{OEIS link|A005114}} || [[Untouchable number]]s || {2, 5, 52, 88, 96, 120, 124, 146, 162, 188, ...}
| Cannot be expressed as the sum of all the proper divisors of any positive integer.
|-
| {{OEIS link|A005132}} || [[Recamán's sequence]] || {0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, ...} || ''"subtract if possible, otherwise add"'': a(0) = 0; for n > 0, a(n) = a(n - 1) - n if that number is positive and not already in the sequence, otherwise a(n) = a(n - 1) + n, whether or not that number is already in the sequence.
|-
| {{OEIS link|A005150}} || [[Look-and-say sequence]] || {1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, 13211311123113112211, ...} || A = 'frequency' followed by 'digit'-indication.
|-
| {{OEIS link|A005153}} || [[Practical number]]s || {1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40...} ||All smaller positive integers can be represented as sums of distinct factors of the number.
|-
| {{OEIS link|A005165}} || [[Alternating factorial]] || {1, 1, 5, 19, 101, 619, 4421, 35899, 326981, 3301819, 36614981, 442386619, 5784634181, 81393657019, ...} || n! - (n-1)! + (n-2)! - ... 1!.
|-
| {{OEIS link|A005224}} || [[Aronson's sequence]] || {1, 4, 11, 16, 24, 29, 33, 35, 39, 45, ...} 
| "t" is the first, fourth, eleventh, ... letter in this sentence, not counting spaces or commas.
|-
| {{OEIS link|A005235}} || [[Fortunate number]]s || {3, 5, 7, 13, 23, 17, 19, 23, 37, 61, ...} 
| The smallest integer {{math|''m'' > 1}} such that {{math|''p''<sub>''n''</sub># + ''m''}} is a prime number, where the primorial {{math|''p''<sub>''n''</sub>#}} is the product of the first {{math|''n''}} prime numbers.
|-
| {{OEIS link|A005349}} || [[Harshad number]]s in base 10  || {1, 2, 3, 4,  5,  6, 7, 8, 9, 10, 12, ...} 
| A Harshad number in base 10 is an integer that is divisible by the sum of its digits (when written in base 10).
|-
| {{OEIS link|A005384}} || Sophie Germain primes || {2, 3, 5, 11, 23, 29, 41, 53, 83, 89, ...} 
| A prime number {{math|''p''}} such that {{math|2''p'' + 1}} is also prime.
|-
| {{OEIS link|A005835}} || [[Semiperfect number]]s || {6, 12, 18, 20, 24, 28, 30, 36, 40, 42, ...} 
| A natural number {{math|''n''}} that is equal to the sum of all or some of its proper divisors.
|-
| {{OEIS link|A006003}} || [[Magic constant]]s || {15, 34, 65, 111, 175, 260, ...} 
| Sum of numbers in any row, column, or diagonal of a magic square of order n = 3, 4, 5, 6, 7, 8, ....
|-
| {{OEIS link|A006037}} || [[Weird number]]s || {70, 836, 4030, 5830, 7192, 7912, 9272, 10430, 10570, 10792, ...} 
| A natural number that is abundant but not semiperfect.
|-
| {{OEIS link|A006842}} || [[Farey sequence]] numerators || {0, 1, 0, 1, 1, 0, 1, 1, 2, 1, ...} || &nbsp; 
|-
| {{OEIS link|A006843}} || [[Farey sequence]] denominators || {1, 1, 1, 2, 1, 1, 3, 2, 3, 1, ...} || &nbsp; 
|-
| {{OEIS link|A006862}} || [[Euclid number]]s || {2, 3, 7, 31, 211, 2311, 30031, 510511, 9699691, 223092871, ...} 
| {{math|''p''<sub>''n''</sub># + 1}}, i.e. {{math|1 + }} product of first {{math|''n''}} consecutive primes.
|-
| {{OEIS link|A006886}} || [[Kaprekar number]]s || {1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728, ...} 
| {{math|''X''<sup>2</sup> {{=}} ''Ab''<sup>''n''</sup> + ''B''}}, where {{math|0 &lt; ''B'' &lt; ''b''<sup>''n''</sup>}} and {{math|''X'' {{=}} ''A'' + ''B''}}.
|-
| {{OEIS link|A007304}} || [[Sphenic number]]s || {30, 42, 66, 70, 78, 102, 105, 110, 114, 130, ...} || Products of 3 distinct primes.
|-
| {{OEIS link|A007318}} || [[Pascal's triangle]] || {1, 1, 1, 1, 2, 1, 1, 3, 3, 1, ...} || Pascal's triangle read by rows.
|-
| {{OEIS link|A007540}} || [[Wilson prime]]s || {5, 13, 563}
|| Primes <math>p</math> satisfying {{math|(''p''-1)! ≡ -1 (mod ''p''<sup>2</sup>)}}.
|-
| {{OEIS link|A007588}} || Stella octangula numbers || {0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990, 2651, 3444, 4381, ...}
| Stella octangula numbers: {{math|''n'' (2''n''<sup>''2''</sup> &minus; 1)}}, with {{math|''n'' &ge; 0}}. 
|-
| {{OEIS link|A007770}} || [[Happy number]]s || {1, 7, 10, 13, 19, 23, 28, 31, 32, 44, ...} 
| The numbers whose trajectory under iteration of sum of squares of digits map includes {{math|1}}.
|-
| {{OEIS link|A007947}} || Radical of an integer || {1, 2, 3, 2, 5, 6, 7, 2, 3, 10, ...} 
| The radical of a positive integer {{math|''n''}} is the product of the distinct prime numbers dividing {{math|''n''}}.
|-
| {{OEIS link|A010060}} || [[Prouhet–Thue–Morse constant]] || {0, 1, 1, 0, 1, 0, 0, 1, 1, 0, ...} 
| <math>\tau = \sum_{i=0}^{\infty} \frac{t_i}{2^{i+1}}.</math>
|-
| {{OEIS link|A014080}} || [[Factorion]]s || {1, 2, 145, 40585, ...} 
| A natural number that equals the sum of the factorials of its decimal digits.
|-
| {{OEIS link|A014577}} || [[Regular paperfolding sequence]] || {1, 1, 0, 1, 1, 0, 0, 1, 1, 1, ...} 
| At each stage an alternating sequence of 1s and 0s is inserted between the terms of the previous sequence.
|-
| {{OEIS link|A016105}} || [[Blum integer]]s || {21, 33, 57, 69, 77, 93, 129, 133, 141, 161, 177, ...} 
| Numbers of the form p * q where p and q are distinct primes congruent to 3 (mod 4).
|-
| {{OEIS link|A016114}} || [[Circular prime]]s || {2, 3, 5, 7, 11, 13, 17, 37, 79, 113, ...} 
| The numbers which remain prime under cyclic shifts of digits.
|-
| {{OEIS link|A018226}} || [[Physics:Magic number|Magic numbers]] || {2, 8, 20, 28, 50, 82, 126, ...} 
| A number of nucleons (either protons or neutrons) such that they are arranged into complete shells within the atomic nucleus.
|-
| {{OEIS link|A019279}} || [[Superperfect number]]s || {2, 4, 16, 64, 4096, 65536, 262144, 1073741824, 1152921504606846976, 309485009821345068724781056, ...} 
| Positive integers {{math|''n''}} for which {{math|''&sigma;''<sup>2</sup>(''n'') {{=}} ''&sigma;''(''&sigma;''(''n'')) {{=}} 2''n''.}}
|-
| {{OEIS link|A027641}} || [[Bernoulli number]]s {{math|''B''<sub>''n''</sub>}} || {1, -1, 1, 0, -1, 0, 1, 0, -1, 0, 5, 0, -691, 0, 7, 0, -3617, 0, 43867, 0, ...} || &nbsp;
|-
| {{OEIS link|A031214}} || First elements in all [[On-Line Encyclopedia of Integer Sequences|OEIS]] sequences || {1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...} || One of sequences referring to the OEIS itself.
|-
| {{OEIS link|A033307}} || Decimal expansion of [[Champernowne constant]] || {1, 2, 3, 4, 5, 6, 7, 8, 9, 1, ...} 
| Formed by concatenating the positive integers.
|-
| {{OEIS link|A034897}} || [[Hyperperfect number]]s || {6, 21, 28, 301, 325, 496, 697, ...} 
| {{math|''k''}}-hyperperfect numbers, i.e. {{math|''n''}} for which the equality {{math|''n'' {{=}} 1 + ''k'' (''σ''(''n'') &minus; ''n'' &minus; 1)}} holds. 
|-
| {{OEIS link|A035513}} || [[Wythoff array]] || {1, 2, 4, 3, 7, 6, 5, 11, 10, 9, ...} 
| A matrix of integers derived from the Fibonacci sequence.
|-
| {{OEIS link|A036262}} || [[Gilbreath's conjecture]] || {2, 1, 3, 1, 2, 5, 1, 0, 2, 7, ...} 
| Triangle of numbers arising from Gilbreath's conjecture.
|-
| {{OEIS link|A037274}} || [[Home prime]] || {1, 2, 3, 211, 5, 23, 7, 3331113965338635107, 311, 773, ...} 
| For {{math|''n'' &ge; 2, ''a''(''n'')}} is the prime that is finally reached when you start with {{math|''n''}}, concatenate its prime factors (A037276) and repeat until a prime is reached; {{math|''a''(''n'') {{=}} &minus; 1}} if no prime is ever reached.
|-
| {{OEIS link|A046075}} || [[Undulating number]]s || {101, 121, 131, 141, 151, 161, 171, 181, 191, 202, ...} 
| A number that has the digit form {{math|''ababab''}}.
|-
| {{OEIS link|A046758}} || [[Equidigital number]]s || {1, 2, 3, 5, 7, 10, 11, 13, 14, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 35, 37, 41, 43, 47, 49, 53, 59, 61, 64, ...} 
| A number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1.
|-
| {{OEIS link|A046760}} || [[Extravagant number]]s || {4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30, 33, 34, 36, 38, ...} 
|  A number that has fewer digits than the number of digits in its [[Integer factorization|prime factorization]] (including [[Exponentiation|exponents]]).
|-
| {{OEIS link|A050278}} || [[Pandigital number]]s || {1023456789, 1023456798, 1023456879, 1023456897, 1023456978, 1023456987, 1023457689, 1023457698, 1023457869, 1023457896, ...} 
| Numbers containing the digits {{math|0&ndash;9}} such that each digit appears exactly once.
|-
| {{OEIS link|A052486}} || [[Achilles number]]s || {72, 108, 200, 288, 392, 432, 500, 648, 675, 800, ...} 
| Positive integers which are powerful but imperfect.
|-
| {{OEIS link|A054037}} || [[Primary pseudoperfect number]]s || {2, 6, 42, 1806, 47058, 2214502422, 52495396602, ...} 
| Satisfies a certain [[Egyptian fraction]].
|-
| {{OEIS link|A059756}} || [[Erdős–Woods number]]s || {16, 22, 34, 36, 46, 56, 64, 66, 70, 76, 78, 86, 88, ...} 
| The length of an interval of consecutive integers with property that every element has a factor in common with one of the endpoints.
|-
| {{OEIS link|A060006}} || Decimal expansion of [[Pisot–Vijayaraghavan number]] || {1, 3, 2, 4, 7, 1, 7, 9, 5, 7, ...} 
| Real root of {{math|''x''<sup>3</sup> &minus; ''x'' &minus; 1}}.
|-
| {{OEIS link|A076336}} || [[Sierpinski number]]s || {78557, 271129, 271577, 322523, 327739, 482719, 575041, 603713, 903983, 934909, ...} 
| Odd {{math|''k''}} for which {{math| { ''k''&sdot;2<sup>''n''</sup> + 1 : ''n'' &isin; ℕ } }} consists only of composite numbers.
|-
| {{OEIS link|A076337}} || [[Riesel number]]s || {509203, 762701, 777149, 790841, 992077, ...} 
| Odd {{math|''k''}} for which {{math| { ''k''&sdot;2<sup>''n''</sup> &minus; 1 : ''n'' &isin; ℕ } }} consists only of composite numbers.
|-
| {{OEIS link|A086747}} || [[Baum–Sweet sequence]] || {1, 1, 0, 1, 1, 0, 0, 1, 0, 1, ...} 
| {{math|''a''(''n'') {{=}} 1}} if the binary representation of {{math|''n''}} contains no block of consecutive zeros of odd length; otherwise {{math|''a''(''n'') {{=}} 0}}.
|-
| {{OEIS link|A088054}} || [[Factorial prime]]s || {2, 3, 5, 7, 23, 719, 5039, 39916801, ...}
| A [[Prime number|prime number]] that is one less or one more than a [[Factorial|factorial]] (all factorials > 1 are even).
|-
| {{OEIS link|A088164}} || [[Wolstenholme prime]]s || {16843, 2124679}
| Primes <math>p</math> satisfying <math>{2p-1 \choose p-1} \equiv 1 \pmod{p^4}</math>.
|-
| {{OEIS link|A090822}} || [[Gijswijt's sequence]] || {1, 1, 2, 1, 1, 2, 2, 2, 3, 1, ...}
| The {{math|''n''}}th term counts the maximal number of repeated blocks at the end of the subsequence from {{math|1}} to {{math|''n''-1}}
|-
| {{OEIS link|A093112}} || [[Carol number]]s || {−1, 7, 47, 223, 959, 3967, 16127, 65023, 261119, 1046527, ...}
| <math>a(n) = (2^n - 1)^2 - 2.</math>
|-
| {{OEIS link|A094683}} || [[Juggler sequence]] || {0, 1, 1, 5, 2, 11, 2, 18, 2, 27, ...} 
| If {{math|''n'' ≡ 0 (mod 2)}} then {{math|⌊{{sqrt|''n''}}⌋}} else {{math|⌊''n''<sup>3/2</sup>⌋}}.
|-
| {{OEIS link|A097942}} || [[Highly totient number]]s || {1, 2, 4, 8, 12, 24, 48, 72, 144, 240, ...} 
| Each number {{math|''k''}} on this list has more solutions to the equation {{math|''&phi;''(''x'') {{=}} ''k''}} than any preceding {{math|''k''}}.
|-
| {{OEIS link|A100264}} || Decimal expansion of [[Chaitin's constant]] || {0, 0, 7, 8, 7, 4, 9, 9, 6, 9, ...} 
| Chaitin constant (Chaitin omega number) or halting probability. 
|-
| {{OEIS link|A104272}} || [[Ramanujan prime]]s || {2, 11, 17, 29, 41, 47, 59, 67, ...} 
| The {{math|''n''}}<sup>th</sup> Ramanujan prime is the least integer {{math|''R''<sub>''n''</sub>}} for which {{math|''&pi;''(''x'') &minus; ''&pi;''(''x''/2) ≥ ''n''}}, for all {{math|''x'' ≥ ''R''<sub>''n''</sub>}}.
|-
| {{OEIS link|A122045}} || [[Euler number]]s || {1, 0, &minus;1, 0, 5, 0, &minus;61, 0, 1385, 0, ...} 
| <math>\frac{1}{\cosh t} = \frac{2}{e^{t} + e^ {-t} } = \sum_{n=0}^\infty  \frac{E_n}{n!} \cdot t^n.</math>
|-
| {{OEIS link|A138591}} || [[Polite number]]s || {3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, ...} 
| A positive integer that can be written as the sum of two or more consecutive positive integers. 
|-
| {{OEIS link|A182369}} || 867-5309/Jenny || {8, 6, 7, 5, 3, 0, 9, ...} 
| Decimal expansion of (7^(e - 1/e) - 9)*Pi^2, also known as Jenny's constant.
|-
| {{OEIS link|A194472}} || [[Erdős–Nicolas number]]s || {24, 2016, 8190, 42336, 45864, 392448, 714240, 1571328, ...} 
| A number {{mvar|n}} such that there exists another number {{mvar|m}} and <math>\sum_{d\mid n,\ d\leq m}d=n.</math> 
|-
|}

==References==
* [http://oeis.org/wiki/Index_to_OEIS:_Section_Cor#core OEIS core sequences]

==External links==
* [http://oeis.org/wiki/Index_to_OEIS Index to OEIS]

{{Series (mathematics)}}

{{DEFAULTSORT:OEIS sequences}}
[[Category:Integer sequences|*]]

{{Sourceattribution|List of OEIS sequences|1}}