10,000

From HandWiki

10,000 (ten thousand) is the natural number following 9,999 and preceding 10,001.

Name

Many languages have a specific word for this number; in Ancient Greek it is μύριοι (the etymological root of the word myriad in English), in Aramaic ܪܒܘܬܐ, in Hebrew רבבה [revava], in Chinese 萬/万 (Mandarin wàn, Cantonese maan6, Hokkien bān), in Japanese 万/萬 [man], in Khmer ម៉ឺន [meun], in Korean 만/萬 [man], in Russian тьма [t'ma], in Vietnamese vạn, in Sanskrit अयुत [ayuta], in Thai หมื่น [meun], in Malayalam പതിനായിരം [patinayiram], and in Malagasy alina.[1] In many of these languages, it often denotes a very large but indefinite number.[2]

The classical Greeks used letters of the Greek alphabet to represent Greek numerals: they used a capital letter mu (Μ) to represent ten thousand. This Greek root was used in early versions of the metric system in the form of the decimal prefix myria-.[3]

Depending on the country, the number ten thousand is usually written as 10,000 (including in the UK and US), 10.000, or 10 000.[4]

In mathematics

In scientific notation, it is written as 104 or 1 E+4 (equivalently 1 E4) in E notation. It is the square of 100 and the square root of 100,000,000.

The value of a myriad to the power of itself, 1000010000 = 1040000.

It has a reduced totient of 500, and a totient of 4,000, with a total of 16 integers having a totient value of 10,000.[5][6]

There are a total of 1,229 prime numbers less than ten thousand, a count that is itself prime.[7][8]

A myriagon is a polygon with ten thousand edges and a total of 25 dihedral symmetry groups when including the myriagon itself, alongside 25 cyclic groups as subgroups.[9]

In science

In time

  • 10000 BC, 10000 BCE, or 10th millennium BC.
  • 10000-year clock or the Clock of the Long Now is a mechanical clock designed to keep time for 10000 years.

In the arts

Visual media

  • 10,000 Black Men Named George, a TV series (2002)
  • The Phantom from 10,000 Leagues, a monster film (1956)
  • Vietnam: The Ten Thousand Day War, a miniseries (1980)

Bands

  • 10,000 Maniacs, an American rock band
  • 10,000 Promises., a J-pop group

Albums

  • 10,000 Days, by Tool (2006)
  • 10,000 Hz Legend, by Air (2001)
  • 10,000 Reasons (album) by Matt Redman (2013)
  • 10,000 Gecs by 100 gecs (2023)
  • Ten Thousand Fists, by Disturbed (2005)

Songs

  • "Ten Thousand Men of Harvard", fight song of Harvard University
  • "10,000 Reasons (Bless the Lord)" by Matt Redman (2013)
  • "Ten Thousand Strong" by Iced Earth (2007)

In other fields

  • In currency,
    • A version of Iraq's 10,000 dinar banknote has Abu Ali Hasan Ibn al-Haitham (also known as Alhazen) on the front, and a later issue has sculptor Jawad Saleem's Freedom Monument in Baghdad on the front. Both notes have an image of Mosul's al-Hadba' Minaret on the back.[18] The first issue had an image of former Iraqi president Saddam Hussein and the Spiral Minaret - Al-Minārat Al-Malwiyyah in Samarra.[19]
    • the Japanese ¥10,000 banknote depicts Fukuzawa Yukichi.
    • Kazakhstan's 10,000₸ banknote.
    • the Lebanese £L10,000 banknote depicts Beirut's Martyrs' Square.
    • Myanmar's (Burma's) Ks.10,000/- banknote.
    • the U.S. $10,000 note depicts a picture of Salmon P. Chase.
  • In distances,
    • 10 km, 10,000 m, or 1 E+4 m is equal to:
      • 1 Scandinavian mil.
      • about 6.2137 English miles.
      • side of square with area 100 km2.
      • radius of a circle with area 100 π km2 ≈ 314.159 km2.
  • In finance, on March 29, 1999, the Dow Jones Industrial Average closed at 10006.78, which was the first time the index closed above the 10,000 mark.
  • In futurology, Stewart Brand in Visions of the Future: The 10,000-Year Library proposes a museum built around a 10,000-year clock as an idea for assuring that vital information survives future crashes of civilizations.[20]
  • In games,
    • Ten Thousand is one name of a dice game called farkle.
  • In game shows, The $10,000 Pyramid ran on television from 1973 to 1974.
  • In history,
    • Army of 10,000 Mississippi American Civil War military unit, 1861–1862.[21]
    • The Army of the Ten Thousand were a group of Ancient Greek mercenaries who marched against Artaxerxes II of Persia.
    • The Persian Immortals were also called the Ten Thousand or 10,000 Immortals, so named because their Number of 10,000 was immediately re-established after every loss.
    • The 10,000 Day War: Vietnam by Michael Maclear ISBN 0-312-79094-5 also alternate titles The ten thousand day war: Vietnam, 1945–1975 (10,000 days is 27.4 years).
    • Tomb of Ten Thousand Soldiers – defeat of the Tang dynasty army of China in the Nanzhao kingdom in 751.
    • In Islamic history, 10,000 is the Number of besieging forces led by Muhammad's adversary, Abu Sufyan, during the Battle of the Trench.
    • 10,000 is the number of Muhammad's soldiers during the conquest of Mecca.
  • In language,
    • the Chinese, Japanese, Korean, and Vietnamese phrase live for ten thousand years was used to bless emperors in East Asia.
    • Μύριοι is an Ancient Greek name for 10.000 taken into the modern European languages as 'myriad' (see above). Hebrew, Chinese, Japanese, and Korean have words with the same meaning.
  • In literature,
    • Man'yōshū (万葉集 Man'yōshū, Collection of Ten Thousand Leaves) is the oldest existing, and most highly revered, collection of Japanese poetry.
    • Ten Thousand a Year 1839 by Samuel Warren.
    • Ten Thousand a Year 1883?. A drama in three acts. Adapted from the celebrated novel of the same name, by the author of the Diary of a Physician, and arranged for the stage by Richard Brinsley Peake.[22]
    • Anabasis, by the Greek writer Xenophon (431–360 B.C.), about the Army of the Ten Thousand – Greek mercenaries taking part in the expedition of Cyrus the Younger, a Persian prince, against his brother, King Artaxerxes II.
    • The Ten Thousand: A Novel of Ancient Greece by Michael Curtis Ford. 2001. ISBN 0-312-26946-3 Historic fiction about the Army of the Ten Thousand.
    • The World of the Ten Thousand Things: Poems 1980–1990 by Charles Wright ISBN 0-374-29293-0 ISBN 0-374-52326-6.
    • Ten Thousand Lovers by Edeet Ravel ISBN 0-06-056562-4.
  • In philosophy, Lao Zi writes about ten thousand things in the Tao Te Ching. In Taoism, the "10,000 Things" is a term meaning all of phenomenal reality.[23]
  • In piphilology, ten thousand is the current world record for the Number of digits of pi memorized by a human being.
  • In psychology, Ten Thousand Dreams Interpreted, or what's in a dream: a scientific and practical, by Miller, Gustavus Hindman (1857–1929). Project Gutenberg.[24]
  • In religion,
    • The Bible,
      • has 52 references to ten thousand in the King James Version.[25]
      • Revelation 5:11 And I beheld, and I heard the voice of many angels round about the throne and the beasts and the elders: and the number of them was ten thousand times ten thousand, and thousands of thousands.[26]
    • hymn, Ten thousand times ten thousand.[27]
    • The Ten thousand martyrs.[28]
  • In software,
    • The Year 10,000 problem is the collective name for all potential software bugs that will emerge as the need to express years with five digits arises.
  • In sports,
    • In athletics, 10,000 meters, 10 kilometers, 10 km, or 10K (6.2 miles) is the final standard track event in a long-distance track event and a distance in other racing events such as running, cycling, and skiing.
    • In bicycle racing, annual Tour of 10,000 Lakes Stage Race in Minneapolis.[29]
    • In baseball, on July 15, 2007, the Philadelphia Phillies became the first team in American professional sports history to lose 10,000 games.

Selected numbers in the range 10001-19999

10001 to 10999

11000 to 11999

  • 11011 = strobogrammatic number[57]
  • 11025 = 1052, the sum of the first 14 positive integer cubes
  • 11083 = palindromic prime in 2 consecutive bases: 23 (KLK23) and 24 (J5J24)
  • 11111 = strobogrammatic number[58]
  • 11297 = number of planar partitions of 16[59]
  • 11298 = Riordan number
  • 11311 = palindromic prime in decimal[45]
  • 11340 = Harshad number in bases 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15 and 16
  • 11353 = star prime[41]
  • 11368 = pentagonal pyramidal number[36]
  • 11410 = weird number[44]
  • 11411 = palindromic prime in decimal[45]
  • 11424 = Harshad number in bases 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15 and 16
  • 11440 = square pyramidal number[42]
  • 11480 = tetrahedral number[48]
  • 11520 = highly totient number[60]
  • 11549 = highly cototient number[40]
  • 11550 = sparsely totient number[52]
  • 11574 = approximate number of days in a billion seconds
  • 11593 = smallest prime to start a run of nine consecutive primes of the form 4k + 1
  • 11605 = smallest integer to start a run of five consecutive integers with the same number of divisors
  • 11664 = 3-smooth number (24×36).
  • 11690 = weird number[44]
  • 11717 = twin prime with 11719
  • 11719 = cuban prime,[39] twin prime with 11717
  • 11726 = octahedral number[43]
  • 11781 = triangular number, hexagonal number, octagonal number, and also 58-gonal, 216-gonal, 329-gonal, 787-gonal and 3928-gonal number[61][62][63]
  • 11811 = strobogrammatic number[64]
  • 11826 = smallest number whose square is pandigital without zeros
  • 11842 = palindromic in bases 3 (1210201213), 27 (G6G27) and 34 (A8A34)
  • 11953 = palindromic prime in bases 7 (465647) and 30 (D8D30)
  • 11970 = sparsely totient number[52]

12000 to 12999

  • 12000 = 12,000 of each of the twelve tribes of Israel made up the 144,000 servants of God who were 'sealed' according to the Book of Revelation in the New Testament[65]
  • 12048 = number of non-isomorphic set-systems of weight 12
  • 12097 = cuban prime[39]
  • 12101 = Friedman prime
  • 12107 = Friedman prime
  • 12109 = Friedman prime
  • 12110 = weird number[44]
  • 12167 = 233
  • 12172 = number of triangle-free graphs on 10 vertices[66]
  • 12180 = sparsely totient number[52]
  • 12198 = semi-meandric number[67]
  • 12251 = number of primes ≤217[68]
  • 12285 = amicable number with 14595
  • 12287 = Thabit number
  • 12288 = 3-smooth number (212×3).
  • 12289 = Proth prime, Pierpont prime
  • 12310 = number of partitions of 34[34]
  • 12321 = 1112, Demlo number, palindromic square
  • 12341 = tetrahedral number[48]
  • 12345 = smallest whole number containing all numbers from 1 to 5
  • 12390 = sparsely totient number[52]
  • 12407 = cited on QI as the smallest uninteresting positive integer regarding arithmetical mathematics[notes 1][69]
  • 12421 = palindromic prime[45]
  • 12496 = smallest sociable number[70]
  • 12500 = 22×55[71]
  • 12529 = square pyramidal number[42]
  • 12530 = weird number[44]
  • 12542 = there is a match puzzle called MOST + MOST = TOKYO, where each letter represents a digit. When one solves the puzzle, TOKYO = 12542, as 6271 + 6271 = 12542 [72]
  • 12670 = weird number[44]
  • 12721 = palindromic prime[45]
  • 12726 = Ruth–Aaron pair
  • 12758 = most significant Number that cannot be expressed as the sum of distinct cubes
  • 12765 = Finnish internet meme; the code accompanying no-prize caps in a Coca-Cola bottle top prize contest. Often spelled out yksi – kaksi – seitsemän – kuusi – viisi, ei voittoa, "one – two – seven – six – five, no prize".
  • 12769 = 1132, palindromic in base 3
  • 12821 = palindromic prime[45]

13000 to 13999

14000 to 14999

15000 to 15999

16000 to 16999

17000 to 17999

18000 to 18999

19000 to 19999

  • 19019 = square pyramidal number[42]
  • 19061 = strobogrammatic number[100]
  • 19110 = sparsely totient number[52]
  • 19116 = sociable number[70]
  • 19141 = unique prime in base 12
  • 19161 = strobogrammatic number[101]
  • 19302 = number of ways to partition {1,2,3,4,5,6,7} and then partition each cell (block) into subcells[102]
  • 19320 = number of trees with 16 unlabeled nodes,[103] sparsely totient number[52]
  • 19390 = weird number[44]
  • 19391 = palindromic prime[45]
  • 19417 = prime sextuplet, along with 19421, 19423, 19427, 19429, and 19433
  • 19441 = cuban prime[39]
  • 19455 = smallest integer that cannot be expressed as a sum of fewer than 548 ninth powers
  • 19513 = tribonacci number[47]
  • 19531 = repunit prime in base 5
  • 19600 = 1402, tetrahedral number
  • 19601/13860 ≈ √2
  • 19609 = first prime followed by a prime gap of over fifty[81]
  • 19670 = weird number[44]
  • 19683 = 273, 39. Furthermore, there is a math puzzle regarding the word logic, such that LOGIC = (L+O+G+I+C)3. The solution to this is (1+9+6+8+3) (1+9+6+8+3) (1+9+6+8+3), which is (27)(27)(27), which equals to 19683. This is one of two digits for which this works, although the other solution has O and I are the same digit: 17576, as (1+7+5+7+6) (1+7+5+7+6) (1+7+5+7+6) = (26)(26)(26) = 17576.[104] It is also a perfect totient number.[82]
  • 19729 is the number of digits in 2↑↑5(Tetration)
  • 19739 = fourth nice Friedman prime
  • 19861 = strobogrammatic prime[85]
  • 19871 = octahedral number[43]
  • 19891 = palindromic prime[45]
  • 19916 = sociable number[70]
  • 19927 = cuban prime[39]
  • 19991 = palindromic prime[45]

Primes

There are 1033 prime numbers between 10000 and 20000, a count that is itself prime. It is 196 prime numbers less than the number of primes between 0 and 10000 (1229, also prime).

See also

Notes

  1. ↑ On the basis that it did not then (November 2011) appear in Sloane's On-Line Encyclopedia of Integer Sequences

References

  1. ↑ "Malagasy Dictionary and Madagascar Encyclopedia : Alina". http://malagasyword.org/bins/teny2/alina. 
  2. ↑ "Myriad Definition & Meaning - Merriam-Webster". 13 March 2024. http://www.merriam-webster.com/dictionary/myriad. 
  3. ↑ Baldwin, James (1885). "Notes on Teaching History". Educational Weekly 5 (2): 4–5. ISSN 2475-3262. https://www.jstor.org/stable/44009109. 
  4. ↑ "Decimal and Thousands Separators (International Language Environments Guide)". https://docs.oracle.com/cd/E19455-01/806-0169/overview-9/index.html. 
  5. ↑ Sloane, N. J. A., ed. "Sequence A002322 (Reduced totient function)". OEIS Foundation. https://oeis.org/A002322. 
  6. ↑ Sloane, N. J. A., ed. "Sequence A000010 (Euler totient function)". OEIS Foundation. https://oeis.org/A000010. 
  7. ↑ Sloane, N. J. A., ed. "Sequence A006880 (Number of primes less than 10^n)". OEIS Foundation. https://oeis.org/A006880. 
  8. ↑ Sloane, N. J. A., ed. "Sequence A000040 (The prime numbers)". OEIS Foundation. https://oeis.org/A000040.  See "Table of n, prime(n) for n = 1..10000" under "Links".
  9. ↑ John Horton Conway; Heidi Burgiel; Chaim Goodman-Strauss (2008). The Symmetries of Things. A K Peters/CRC Press. ISBN 978-1-56881-220-5. https://www.routledge.com/The-Symmetries-of-Things/Conway-Burgiel-Goodman-Strauss/p/book/9781568812205.  Chapter 20.
  10. ↑ Template:Deprecated archive
  11. ↑ news
  12. ↑ "NASA Project: Columbia". http://www.nas.nasa.gov/About/Projects/Columbia/columbia.html. 
  13. ↑ 10000 trails web site[Usurped!]
  14. ↑ "Ten Thousand Islands NWR". http://southeast.fws.gov/TenThousandIsland/. 
  15. ↑ Brewster, David (1830). The Edinburgh Encyclopædia. 12. Edinburgh, UK: William Blackwood, John Waugh, John Murray, Baldwin & Cradock, J. M. Richardson. p. 494. https://books.google.com/books?id=0bIkTUZAbxcC. Retrieved 2015-10-09. 
  16. ↑ Brewster, David (1832). The Edinburgh Encyclopaedia. 12 (1st American ed.). Joseph and Edward Parker. https://books.google.com/books?id=17RGAQAAIAAJ&pg=PA572. Retrieved 2015-10-09. 
  17. ↑ Dingler, Johann Gottfried (1823) (in de). Polytechnisches Journal. 11. Stuttgart, Germany: J.W. Gotta'schen Buchhandlung. https://books.google.com/books?id=wF3zAAAAMAAJ&pg=PA500. Retrieved 2015-10-09. 
  18. ↑ "Iraq Dinar Currency Photos| Banknote Series | 25000, 10000, 5000, 1000, 250, 50 Dinars". iraqi-dinar.com. http://www.iraqi-dinar.com/dinar-currency.php. 
  19. ↑ http://www.iraqsales.com/10%2C000.htm
  20. ↑ Brand, Stewart. "The 10,000-Year Library". http://www.kurzweilai.net/meme/frame.html?main=%2Farticles%2Fart0158.html. 
  21. ↑ "Army of 10,000". http://mississippiscv.org/MS_Units/army_of_10k.htm. 
  22. ↑ "University of Michigan Digital Library - Login Options". http://www.hti.umich.edu/cgi/b/bib/bibperm?q1=eprosed-P3.0504. 
  23. ↑ "Tao Te Ching, Verse 34". http://www.thebigview.com/tao-te-ching/chapter34.html. 
  24. ↑ https://www.gutenberg.org/ebooks/926 : Ten Thousand Dreams Interpreted
  25. ↑ http://bible.gospelcom.net/keyword/?search=ten%20thousand&version1=9&searchtype=phrase&wholewordsonly=yes , [1]
  26. ↑ (KJV) The Apocalypse of John
  27. ↑ "Ten Thousand Times Ten Thousand". https://hymnary.org/text/ten_thousand_times_ten_thousand_in_spark. 
  28. ↑ The Catholic Encyclopedia
  29. ↑ Ulmer, Jeanne. "Minnesota Cycling Team –Tour of 10,000 Lakes". http://www.tourof10000lakes.net/. 
  30. ↑ Sloane, N. J. A., ed. "Sequence A000787 (Strobogrammatic numbers)". OEIS Foundation. https://oeis.org/A000787. 
  31. ↑ Sloane, N. J. A., ed. "Sequence A006982 (Number of unlabeled distributive lattices on n nodes)". OEIS Foundation. https://oeis.org/A006982. 
  32. ↑ 32.0 32.1 Sloane, N. J. A., ed. "Sequence A002182 (Highly composite numbers)". OEIS Foundation. https://oeis.org/A002182. 
  33. ↑ Sloane, N. J. A., ed. "Sequence A000787 (Strobogrammatic numbers)". OEIS Foundation. https://oeis.org/A000787. 
  34. ↑ 34.0 34.1 34.2 34.3 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. 
  35. ↑ Sloane, N. J. A., ed. "Sequence A273987 (Smallest Riesel number to base n)". OEIS Foundation. https://oeis.org/A273987. 
  36. ↑ 36.0 36.1 36.2 36.3 36.4 Sloane, N. J. A., ed. "Sequence A002411 (Pentagonal pyramidal numbers)". OEIS Foundation. https://oeis.org/A002411. 
  37. ↑ Sloane, N. J. A., ed. "Sequence A003261 (Woodall (or Riesel) numbers: n*2^n - 1)". OEIS Foundation. https://oeis.org/A003261. 
  38. ↑ 38.0 38.1 38.2 Sloane, N. J. A., ed. "Sequence A000931 (Padovan sequence)". OEIS Foundation. https://oeis.org/A000931. 
  39. ↑ 39.0 39.1 39.2 39.3 39.4 39.5 39.6 39.7 Sloane, N. J. A., ed. "Sequence A002407 (Cuban primes)". OEIS Foundation. https://oeis.org/A002407. 
  40. ↑ 40.00 40.01 40.02 40.03 40.04 40.05 40.06 40.07 40.08 40.09 40.10 40.11 Cite error: Invalid <ref> tag; no text was provided for refs named A100827
  41. ↑ 41.0 41.1 41.2 Sloane, N. J. A., ed. "Sequence A083577 (Prime star numbers)". OEIS Foundation. https://oeis.org/A083577. 
  42. ↑ 42.0 42.1 42.2 42.3 42.4 42.5 42.6 42.7 Sloane, N. J. A., ed. "Sequence A000330 (Square pyramidal numbers)". OEIS Foundation. https://oeis.org/A000330. 
  43. ↑ 43.0 43.1 43.2 43.3 43.4 43.5 43.6 Sloane, N. J. A., ed. "Sequence A005900 (Octahedral numbers)". OEIS Foundation. https://oeis.org/A005900. 
  44. ↑ 44.00 44.01 44.02 44.03 44.04 44.05 44.06 44.07 44.08 44.09 44.10 44.11 44.12 44.13 44.14 44.15 44.16 44.17 44.18 44.19 44.20 44.21 44.22 44.23 44.24 44.25 44.26 44.27 Sloane, N. J. A., ed. "Sequence A006037 (Weird numbers)". OEIS Foundation. https://oeis.org/A006037. 
  45. ↑ 45.00 45.01 45.02 45.03 45.04 45.05 45.06 45.07 45.08 45.09 45.10 45.11 45.12 45.13 45.14 45.15 45.16 45.17 45.18 45.19 45.20 45.21 45.22 45.23 Sloane, N. J. A., ed. "Sequence A002385 (Palindromic primes: prime numbers whose decimal expansion is a palindrome)". OEIS Foundation. https://oeis.org/A002385. 
  46. ↑ 46.0 46.1 Sloane, N. J. A., ed. "Sequence A002997 (Carmichael numbers)". OEIS Foundation. https://oeis.org/A002997. 
  47. ↑ 47.0 47.1 Sloane, N. J. A., ed. "Sequence A000073 (Tribonacci numbers)". OEIS Foundation. https://oeis.org/A000073. 
  48. ↑ 48.0 48.1 48.2 48.3 48.4 48.5 Sloane, N. J. A., ed. "Sequence A000292 (Tetrahedral numbers)". OEIS Foundation. https://oeis.org/A000292. 
  49. ↑ Sloane, N. J. A., ed. "Sequence A000078 (Tetranacci numbers)". OEIS Foundation. https://oeis.org/A000078. 
  50. ↑ Sloane, N. J. A., ed. "Sequence A000787 (Strobogrammatic numbers)". OEIS Foundation. https://oeis.org/A000787. 
  51. ↑ Sloane, N. J. A., ed. "Sequence A001190 (Wedderburn-Etherington numbers)". OEIS Foundation. https://oeis.org/A001190. 
  52. ↑ 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 52.13 Cite error: Invalid <ref> tag; no text was provided for refs named A036913
  53. ↑ 53.0 53.1 Sloane, N. J. A., ed. "Sequence A000045 (Fibonacci numbers)". OEIS Foundation. https://oeis.org/A000045. 
  54. ↑ 54.0 54.1 Sloane, N. J. A., ed. "Sequence A002559 (Markoff (or Markov) numbers)". OEIS Foundation. https://oeis.org/A002559. 
  55. ↑ Taneja, Inder (2013). "Crazy Sequential Representation: Numbers from 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9". arXiv:1302.1479 [math.HO].
  56. ↑ Sloane, N. J. A., ed. "Sequence A000014 (Number of series-reduced trees with n nodes)". OEIS Foundation. https://oeis.org/A000014. 
  57. ↑ Sloane, N. J. A., ed. "Sequence A000787 (Strobogrammatic numbers)". OEIS Foundation. https://oeis.org/A000787. 
  58. ↑ Sloane, N. J. A., ed. "Sequence A000787 (Strobogrammatic numbers)". OEIS Foundation. https://oeis.org/A000787. 
  59. ↑ 59.0 59.1 Sloane, N. J. A., ed. "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". OEIS Foundation. https://oeis.org/A000219. 
  60. ↑ 60.0 60.1 Sloane, N. J. A., ed. "Sequence A097942 (Highly totient numbers)". OEIS Foundation. https://oeis.org/A097942. 
  61. ↑ Sloane, N. J. A., ed. "Sequence A000217 (Triangular numbers)". OEIS Foundation. https://oeis.org/A000217. 
  62. ↑ Sloane, N. J. A., ed. "Sequence A000384 (Hexagonal numbers)". OEIS Foundation. https://oeis.org/A000384. 
  63. ↑ Sloane, N. J. A., ed. "Sequence A000567 (Octagonal numbers)". OEIS Foundation. https://oeis.org/A000567. 
  64. ↑ Sloane, N. J. A., ed. "Sequence A000787 (Strobogrammatic numbers)". OEIS Foundation. https://oeis.org/A000787. 
  65. ↑ Revelation 7:4-8
  66. ↑ Sloane, N. J. A., ed. "Sequence A006785 (Number of triangle-free graphs on n vertices)". OEIS Foundation. https://oeis.org/A006785. 
  67. ↑ Sloane, N. J. A., ed. "Sequence A000682 (Semimeanders)". OEIS Foundation. https://oeis.org/A000682. 
  68. ↑ Sloane, N. J. A., ed. "Sequence A007053 (Number of primes <= 2^n)". OEIS Foundation. https://oeis.org/A007053. 
  69. ↑ Host: Stephen Fry; Panellists: Alan Davies, Al Murray, Dara Ó Briain and Sandi Toksvig (11 November 2011). "Inland Revenue". QI. Series I. Episode 10. London, England. 19:55 minutes in. BBC. BBC Two.
  70. ↑ 70.0 70.1 70.2 70.3 70.4 70.5 70.6 70.7 70.8 Cite error: Invalid <ref> tag; no text was provided for refs named A122726
  71. ↑ Sloane, N. J. A., ed. "Sequence A048102 (Numbers k such that if k equals Product p_i^e_i then p_i equals e_i for all i)". OEIS Foundation. https://oeis.org/A048102. 
  72. ↑ "MOST+MOST Puzzle - Solution". https://www.mathsisfun.com/puzzles/most-most-solution.html. 
  73. ↑ Sloane, N. J. A., ed. "Sequence A000011 (Number of n-bead necklaces (turning over is allowed) where complements are equivalent)". OEIS Foundation. https://oeis.org/A000011. 
  74. ↑ Sloane, N. J. A., ed. "Sequence A000013 (Definition (1): Number of n-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed)". OEIS Foundation. https://oeis.org/A000013. 
  75. ↑ Sloane, N. J. A., ed. "Sequence A000129 (Pell numbers)". OEIS Foundation. https://oeis.org/A000129. 
  76. ↑ Sloane, N. J. A., ed. "Sequence A112643 (Odd and square-free abundant numbers)". OEIS Foundation. https://oeis.org/A112643. 
  77. ↑ "A002182 - OEIS". https://oeis.org/A002182. 
  78. ↑ Sloane, N. J. A., ed. "Sequence A051015 (Zeisel numbers)". OEIS Foundation. https://oeis.org/A051015. 
  79. ↑ Sloane, N. J. A., ed. "Sequence A001006 (Motzkin numbers)". OEIS Foundation. https://oeis.org/A001006. 
  80. ↑ 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. 
  81. ↑ 81.0 81.1 "Table of Known Maximal Gaps". Prime Pages. https://primes.utm.edu/notes/GapsTable.html. 
  82. ↑ 82.0 82.1 Cite error: Invalid <ref> tag; no text was provided for refs named A082897
  83. ↑ 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. 
  84. ↑ Sloane, N. J. A., ed. "Sequence A002104 (Logarithmic numbers)". OEIS Foundation. https://oeis.org/A002104. 
  85. ↑ 85.0 85.1 85.2 Sloane, N. J. A., ed. "Sequence A007597 (Strobogrammatic primes)". OEIS Foundation. https://oeis.org/A007597. 
  86. ↑ Sloane, N. J. A., ed. "Sequence A000787 (Strobogrammatic numbers)". OEIS Foundation. https://oeis.org/A000787. 
  87. ↑ 87.0 87.1 Sloane, N. J. A., ed. "Sequence A076980 (Leyland numbers)". OEIS Foundation. https://oeis.org/A076980. 
  88. ↑ Sloane, N. J. A., ed. "Sequence A005276 (Betrothed (or quasi-amicable) numbers.)". OEIS Foundation. https://oeis.org/A005276. 
  89. ↑ Sloane, N. J. A., ed. "Sequence A000108 (Catalan numbers)". OEIS Foundation. https://oeis.org/A000108. 
  90. ↑ Sloane, N. J. A., ed. "Sequence A088164 (Wolstenholme primes)". OEIS Foundation. https://oeis.org/A088164. 
  91. ↑ Sloane, N. J. A., ed. "Sequence A000787 (Strobogrammatic numbers)". OEIS Foundation. https://oeis.org/A000787. 
  92. ↑ Sloane, N. J. A., ed. "Sequence A000112 (Number of partially ordered sets (posets) with n unlabeled elements)". OEIS Foundation. https://oeis.org/A000112. 
  93. ↑ 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. 
  94. ↑ Sloane, N. J. A., ed. "Sequence A006886 (Kaprekar numbers)". OEIS Foundation. https://oeis.org/A006886. 
  95. ↑ Sloane, N. J. A., ed. "Sequence A000787 (Strobogrammatic numbers)". OEIS Foundation. https://oeis.org/A000787. 
  96. ↑ Higgins, ibid.
  97. ↑ 97.0 97.1 Sloane, N. J. A., ed. "Sequence A001599 (Harmonic or Ore numbers)". OEIS Foundation. https://oeis.org/A001599. 
  98. ↑ 98.0 98.1 Sloane, N. J. A., ed. "Sequence A186311 (Least century 100k to 100k+99 with exactly n primes)". OEIS Foundation. https://oeis.org/A186311. 
  99. ↑ Sloane, N. J. A., ed. "Sequence A000787 (Strobogrammatic numbers)". OEIS Foundation. https://oeis.org/A000787. 
  100. ↑ Sloane, N. J. A., ed. "Sequence A000787 (Strobogrammatic numbers)". OEIS Foundation. https://oeis.org/A000787. 
  101. ↑ Sloane, N. J. A., ed. "Sequence A000787 (Strobogrammatic numbers)". OEIS Foundation. https://oeis.org/A000787. 
  102. ↑ Sloane, N. J. A., ed. "Sequence A000258 (Expansion of e.g.f. exp(exp(exp(x)-1)-1))". OEIS Foundation. https://oeis.org/A000258. 
  103. ↑ Sloane, N. J. A., ed. "Sequence A000055 (Number of trees with n unlabeled nodes)". OEIS Foundation. https://oeis.org/A000055. 
  104. ↑ "Algebra LOGIC 2 Puzzle - Solution". https://www.mathsisfun.com/puzzles/algebra-logic-2-solution.htmlsolution.