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10,000

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← 9999 10000 10001 →
Cardinalten thousand
Ordinal10000th
(ten thousandth)
Numeral systemdecamillesimal
Factorization24 × 54
Divisors25 total
Greek numeral
Roman numeralX
Unicode symbol(s)X, ↂ
Greek prefixmyria-
Latin prefixdecamilli-
Binary100111000100002
Ternary1112011013
Senary1141446
Octal234208
Duodecimal595412
Hexadecimal271016
Chinese numeral万, 萬
ArmenianՕ
Egyptian hieroglyph𓂭

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

Name

[edit]

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.[citation needed] 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

[edit]

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 total of 25 divisors, whose geometric mean is a whole number, 100 (the number of primes below this value is 25).[5]

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.[6][7]

There are a total of 1,229 prime numbers less than ten thousand, a count that is itself prime.[5][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

[edit]

In time

[edit]

In the arts

[edit]

In other fields

[edit]
  • In currency,
  • In distances,
  • 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,
  • 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,
  • 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,

Selected numbers in the range 10001-19999

[edit]

10001 to 10999

[edit]

11000 to 11999

[edit]
  • 11025 = 1052, the sum of the first 14 positive integer cubes
  • 11083 = palindromic prime in 2 consecutive bases: 23 (KLK23) and 24 (J5J24)
  • 11111 = Repunit[51]
  • 11297 = Number of planar partitions of 16[52]
  • 11298 = Riordan number
  • 11311 = palindromic prime in decimal[41]
  • 11340 = Harshad number in bases 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15 and 16
  • 11353 = star prime[37]
  • 11368 = pentagonal pyramidal number[33]
  • 11410 = weird number[40]
  • 11411 = palindromic prime in decimal[41]
  • 11424 = Harshad number in bases 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15 and 16
  • 11440 = square pyramidal number[38]
  • 11480 = tetrahedral number[44]
  • 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[40]
  • 11717 = twin prime with 11719
  • 11719 = cuban prime,[36] twin prime with 11717
  • 11726 = octahedral number[39]
  • 11781 = Triangular number, Hexagonal number, Octagonal number, and also 58-gonal, 216-gonal, 329-gonal, 787-gonal and 3928-gonal number[53][54][55]
  • 11826 = smallest number whose square is pandigital without zeros
  • 11953 = palindromic prime in bases 7 (465647) and 30 (D8D30)

12000 to 12999

[edit]
  • 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[56]
  • 12048 = number of non-isomorphic set-systems of weight 12
  • 12097 = cuban prime[36]
  • 12101 = Friedman prime
  • 12107 = Friedman prime
  • 12109 = Friedman prime
  • 12110 = weird number[40]
  • 12167 = 233
  • 12172 = number of triangle-free graphs on 10 vertices[57]
  • 12198 = semi-meandric number[58]
  • 12251 = number of primes [59]
  • 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[31]
  • 12321 = 1112, Demlo number, palindromic square
  • 12341 = tetrahedral number[44]
  • 12345 = smallest whole number containing all numbers from 1 to 5
  • 12407 = cited on Q.I. as the smallest uninteresting positive integer regarding arithmetical mathematics[notes 1][60]
  • 12421 = palindromic prime[41]
  • 12496 = smallest sociable number
  • 12500 = 22×55[61]
  • 12529 = square pyramidal number[38]
  • 12530 = weird number[40]
  • 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 [62]
  • 12670 = weird number[40]
  • 12721 = palindromic prime[41]
  • 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 yksikaksiseitsemänkuusiviisi, ei voittoa, "one – two – seven – six – five, no prize".
  • 12769 = 1132, palindromic in base 3
  • 12821 = palindromic prime[41]

13000 to 13999

[edit]
  • 13122 = 3-smooth number (2×38).
  • 13131 = octahedral number[39]
  • 13244 = tetrahedral number[44]
  • 13267 = cuban prime[36]
  • 13331 = palindromic prime[41]
  • 13370 = weird number[40]
  • 13510 = weird number[40]
  • 13581 = Padovan number[35]
  • 13648 = number of 20-bead necklaces (turning over is allowed) where complements are equivalent[63]
  • 13669 = cuban prime[36]
  • 13685 = square pyramidal number[38]
  • 13790 = weird number[40]
  • 13792 = largest number that is not a sum of 16 fourth powers
  • 13798 = number of 19-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed[64]
  • 13820 = meandric number, open meandric number
  • 13824 = 243
  • 13831 = palindromic prime[41]
  • 13860 = Pell number[65]
  • 13930 = weird number[40]
  • 13931 = palindromic prime
  • 13950 = pentagonal pyramidal number[33]

14000 to 14999

[edit]
  • 14190 = tetrahedral number[44]
  • 14200 = number of n-Queens Problem solutions for n – 12
  • 14341 = palindromic prime[41]
  • 14400 = 1202, the sum of the first 15 positive integers cubes
  • 14595 = amicable number with 12285
  • 14641 = 1212 = 114, palindromic square (base 10)
  • 14644 = octahedral number[39]
  • 14701 = Markov number[48]
  • 14741 = palindromic prime[41]
  • 14770 = weird number[40]
  • 14883 = number of partitions of 35[31]
  • 14884 = 1222, palindromic square in base 11
  • 14910 = square pyramidal number[38]

15000 to 15999

[edit]
  • 15015 = smallest odd and square-free abundant number[66]
  • 15120 = highly composite number; smallest number with exactly 80 factors[30]
  • 15180 = tetrahedral number[44]
  • 15376 = 1242, pentagonal pyramidal number[33]
  • 15387 = Zeisel number[67]
  • 15451 = palindromic prime[41]
  • 15511 = Motzkin prime[68]
  • 15551 = palindromic prime[41]
  • 15552 = 3-smooth number (26×35)
  • 15610 = weird number[40]
  • 15625 = 1252 = 253 = 56
  • 15629 = Friedman prime
  • 15640 = initial number of only four-, five-, or six-digit century to contain two prime quadruples[69] (in between which lies a record prime gap of 43[70])
  • 15661 = Friedman prime
  • 15667 = second nice Friedman prime
  • 15679 = Friedman prime
  • 15793 – Number of parallelogram polyominoes with 13 cells[71]
  • 15841 = Carmichael number[42]
  • 15876 = 1262, palindromic square in base 5
  • 15890 = weird number[40]

16000 to 16999

[edit]

17000 to 17999

[edit]
  • 17073 = number of free 11-ominoes
  • 17163 = the most significant number that is not the sum of the squares of distinct primes
  • 17272 = weird number[40]
  • 17296 = amicable number with 18416[78]
  • 17344 = Kaprekar number[79]
  • 17389 = 2000th prime number
  • 17471 = palindromic prime[41]
  • 17496 = 3-smooth number (23×37)
  • 17570 = weird number[40]
  • 17575 = square pyramidal number[38]
  • 17576 = 263, palindromic in base 5
  • 17689 = 1332, palindromic in base 11
  • 17711 = Fibonacci number[47]
  • 17971 = palindromic prime[41]
  • 17977 = number of partitions of 36[31]
  • 17990 = weird number[40]
  • 17991 = Padovan number[35]

18000 to 18999

[edit]
  • 18010 = octahedral number[39]
  • 18181 = palindromic prime,[41] strobogrammatic prime[73]
  • 18334 = number of planar partitions of 17[52]
  • 18410 = weird number[40]
  • 18416 = amicable number with 17296[80]
  • 18432 = 3-smooth number (211×32).
  • 18481 = palindromic prime[41]
  • 18496 = 1362, the sum of the first 16 positive integers cubes
  • 18600 = harmonic divisor number[81]
  • 18620 = harmonic divisor number[81]
  • 18785 = Leyland number[74] using 4 & 7 (47 + 47)
  • 18830 = weird number[40]
  • 18970 = weird number[40]

19000 to 19999

[edit]
  • 19019 = square pyramidal number[38]
  • 19141 = unique prime in base 12
  • 19302 = Number of ways to partition {1,2,3,4,5,6,7} and then partition each cell (block) into subcells[82]
  • 19320 = number of trees with 16 unlabeled nodes[83]
  • 19390 = weird number[40]
  • 19391 = palindromic prime[41]
  • 19417 = prime sextuplet, along with 19421, 19423, 19427, 19429, and 19433
  • 19441 = cuban prime[36]
  • 19455 = smallest integer that cannot be expressed as a sum of fewer than 548 ninth powers
  • 19513 = tribonacci number[43]
  • 19531 = repunit prime in base 5
  • 19600 = 1402, tetrahedral number
  • 19601/13860 ≈ √2
  • 19609 = first prime followed by a prime gap of over fifty[70]
  • 19670 = weird number[40]
  • 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.[84]
  • 19729 is the number of digits in (Tetration)
  • 19739 = fourth nice Friedman prime
  • 19871 = octahedral number[39]
  • 19891 = palindromic prime[41]
  • 19927 = cuban prime[36]
  • 19991 = palindromic prime[41]

Primes

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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

[edit]

Notes

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

References

[edit]
  1. ^ "Malagasy Dictionary and Madagascar Encyclopedia : Alina".
  2. ^ "Myriad Definition & Meaning - Merriam-Webster". Merriam-Webster's Online Dictionary. 13 March 2024.
  3. ^ Baldwin, James (1885). "Notes on Teaching History". Educational Weekly. 5 (2): 4–5. ISSN 2475-3262. JSTOR 44009109.
  4. ^ "Decimal and Thousands Separators (International Language Environments Guide)". oracle.com.
  5. ^ a b Sloane, N. J. A. (ed.). "Sequence A006880 (Number of primes less than 10^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A002322 (Reduced totient function)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^ Sloane, N. J. A. (ed.). "Sequence A000010 (Euler totient function)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. ^ Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 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. Chapter 20.
  10. ^ Climate Timeline Information Tool
  11. ^ news
  12. ^ "NASA Project: Columbia". Archived from the original on 2005-04-08. Retrieved 2005-02-15.
  13. ^ 10000 trails web site
  14. ^ "Ten Thousand Islands NWR". U.S. Fish & Wildlife Service. Archived from the original on 2005-03-01. Retrieved 2005-02-14.
  15. ^ Brewster, David (1830). The Edinburgh Encyclopædia. Vol. 12. Edinburgh, UK: William Blackwood, John Waugh, John Murray, Baldwin & Cradock, J. M. Richardson. p. 494. Retrieved 2015-10-09.
  16. ^ Brewster, David (1832). The Edinburgh Encyclopaedia. Vol. 12 (1st American ed.). Joseph and Edward Parker. Retrieved 2015-10-09.
  17. ^ Dingler, Johann Gottfried (1823). Polytechnisches Journal (in German). Vol. 11. Stuttgart, Germany: J.W. Gotta'schen Buchhandlung. Retrieved 2015-10-09.
  18. ^ "Iraq Dinar Currency Photos| Banknote Series | 25000, 10000, 5000, 1000, 250, 50 Dinars". iraqi-dinar.com. Archived from the original on 2005-02-07. Retrieved 2022-08-04.
  19. ^ http://www.iraqsales.com/10%2C000.htm Archived 2005-02-06 at the Wayback Machine
  20. ^ Brand, Stewart. "The 10,000-Year Library". kurzweilai.net. Archived from the original on 2005-02-05. Retrieved 2022-08-04.
  21. ^ "Army of 10,000". mississippiscv.org. Archived from the original on 2002-04-01. Retrieved 2022-08-04.
  22. ^ "University of Michigan Digital Library - Login Options".
  23. ^ "Tao Te Ching, Verse 34". thebigview.com. Archived from the original on 2007-08-17. Retrieved 2022-08-04.
  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. ^ [2][dead link]
  28. ^ The Catholic Encyclopedia
  29. ^ Ulmer, Jeanne. "Minnesota Cycling Team –Tour of 10,000 Lakes". tourof10000lakes.net. Archived from the original on 2005-02-21. Retrieved 2022-08-04.
  30. ^ a b Sloane, N. J. A. (ed.). "Sequence A002182 (Highly composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  31. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A000041 (a(n) is the number of partitions of n (the partition numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  32. ^ Sloane, N. J. A. (ed.). "Sequence A273987 (Smallest Riesel number to base n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  33. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A002411 (Pentagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  34. ^ Sloane, N. J. A. (ed.). "Sequence A003261 (Woodall (or Riesel) numbers: n*2^n - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  35. ^ a b c Sloane, N. J. A. (ed.). "Sequence A000931 (Padovan sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  36. ^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A002407 (Cuban primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  37. ^ a b c Sloane, N. J. A. (ed.). "Sequence A083577 (Prime star numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  38. ^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  39. ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A005900 (Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  40. ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab Sloane, N. J. A. (ed.). "Sequence A006037 (Weird numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  41. ^ a b c d e f g h i j k l m n o p q r s t u v w x Sloane, N. J. A. (ed.). "Sequence A002385 (Palindromic primes: prime numbers whose decimal expansion is a palindrome)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  42. ^ a b Sloane, N. J. A. (ed.). "Sequence A002997 (Carmichael numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  43. ^ a b Sloane, N. J. A. (ed.). "Sequence A000073 (Tribonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  44. ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  45. ^ Sloane, N. J. A. (ed.). "Sequence A000078 (Tetranacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  46. ^ Sloane, N. J. A. (ed.). "Sequence A001190 (Wedderburn-Etherington numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  47. ^ a b Sloane, N. J. A. (ed.). "Sequence A000045 (Fibonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  48. ^ a b Sloane, N. J. A. (ed.). "Sequence A002559 (Markoff (or Markov) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  49. ^ 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].
  50. ^ Sloane, N. J. A. (ed.). "Sequence A000014 (Number of series-reduced trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  51. ^ Sloane, N. J. A. (ed.). "Sequence A002275 (Repunits: (10^n - 1)/9. Often denoted by R_n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  52. ^ a b Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  53. ^ Sloane, N. J. A. (ed.). "Sequence A000217 (Triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  54. ^ Sloane, N. J. A. (ed.). "Sequence A000384 (Hexagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  55. ^ Sloane, N. J. A. (ed.). "Sequence A000567 (Octagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  56. ^ Revelation 7:4–8
  57. ^ Sloane, N. J. A. (ed.). "Sequence A006785 (Number of triangle-free graphs on n vertices)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  58. ^ Sloane, N. J. A. (ed.). "Sequence A000682 (Semimeanders)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  59. ^ Sloane, N. J. A. (ed.). "Sequence A007053 (Number of primes <= 2^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  60. ^ 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.
  61. ^ 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)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  62. ^ "MOST+MOST Puzzle - Solution".
  63. ^ Sloane, N. J. A. (ed.). "Sequence A000011 (Number of n-bead necklaces (turning over is allowed) where complements are equivalent)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  64. ^ 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)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  65. ^ Sloane, N. J. A. (ed.). "Sequence A000129 (Pell numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  66. ^ Sloane, N. J. A. (ed.). "Sequence A112643 (Odd and square-free abundant numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  67. ^ Sloane, N. J. A. (ed.). "Sequence A051015 (Zeisel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  68. ^ Sloane, N. J. A. (ed.). "Sequence A001006 (Motzkin numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  69. ^ Sloane, N. J. A. (ed.). "Sequence A007530 (Prime quadruples: numbers k such that k, k+2, k+6, k+8 are all prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  70. ^ a b "Table of Known Maximal Gaps". Prime Pages.
  71. ^ Sloane, N. J. A. (ed.). "Sequence A006958 (Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  72. ^ Sloane, N. J. A. (ed.). "Sequence A002104 (Logarithmic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  73. ^ a b Sloane, N. J. A. (ed.). "Sequence A007597 (Strobogrammatic primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  74. ^ a b Sloane, N. J. A. (ed.). "Sequence A076980 (Leyland numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  75. ^ Sloane, N. J. A. (ed.). "Sequence A000108 (Catalan numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  76. ^ Sloane, N. J. A. (ed.). "Sequence A088164 (Wolstenholme primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  77. ^ Sloane, N. J. A. (ed.). "Sequence A000112 (Number of partially ordered sets (posets) with n unlabeled elements)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  78. ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 61. ISBN 978-1-84800-000-1.
  79. ^ Sloane, N. J. A. (ed.). "Sequence A006886 (Kaprekar numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  80. ^ Higgins, ibid.
  81. ^ a b Sloane, N. J. A. (ed.). "Sequence A001599 (Harmonic or Ore numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  82. ^ Sloane, N. J. A. (ed.). "Sequence A000258 (Expansion of e.g.f. exp(exp(exp(x)-1)-1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  83. ^ Sloane, N. J. A. (ed.). "Sequence A000055 (Number of trees with n unlabeled nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  84. ^ "Algebra LOGIC 2 Puzzle - Solution".
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