Jump to content

2000 (number): Difference between revisions

From Wikipedia, the free encyclopedia
Browse history interactively
← Previous editNext edit →
Content deleted Content added
VisualWikitext
m Reverted edits by Level 6072 (talk) to last version by RMCD bot
Tags: Rollback Reverted
m Undid revision 1224055505 by TAnthony (talk)
Tags: Undo Reverted references removed
Line 42: Line 42:
* '''2022''' – non-isomorphic colorings of a toroidal 3 × 3 grid using exactly three colors under translational symmetry,<ref>{{cite OEIS|A294685|non-isomorphic colorings of a toroidal n X k grid using exactly three colors under translational symmetry}}</ref> beginning of a run of 4 consecutive Niven numbers<ref>{{cite OEIS|A141769|Beginning of a run of 4 consecutive Niven (or Harshad) numbers}}</ref>
* '''2022''' – non-isomorphic colorings of a toroidal 3 × 3 grid using exactly three colors under translational symmetry,<ref>{{cite OEIS|A294685|non-isomorphic colorings of a toroidal n X k grid using exactly three colors under translational symmetry}}</ref> beginning of a run of 4 consecutive Niven numbers<ref>{{cite OEIS|A141769|Beginning of a run of 4 consecutive Niven (or Harshad) numbers}}</ref>
* '''2023''' = 7 * 17 * 17 – multiple of 7 with digit sum equal to 7,<ref>{{cite OEIS|A063416|Multiples of 7 whose sum of digits is equal to 7}}</ref> sum of squares of digits equals 17
* '''2023''' = 7 * 17 * 17 – multiple of 7 with digit sum equal to 7,<ref>{{cite OEIS|A063416|Multiples of 7 whose sum of digits is equal to 7}}</ref> sum of squares of digits equals 17
* '''2024''' – [[tetrahedral number]]<ref name=":1">{{Cite OEIS|A000292|Tetrahedral numbers}}</ref>
* '''2025''' = 45<sup>2</sup>, sum of the cubes of the first nine positive integers (and therefore square of the sum of the first nine positive integers), [[centered octagonal number]]<ref name=":2">{{Cite OEIS|1=A016754|2=Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers}}</ref>
* '''2025''' = 45<sup>2</sup>, sum of the cubes of the first nine positive integers (and therefore square of the sum of the first nine positive integers), [[centered octagonal number]]<ref name=":2">{{Cite OEIS|1=A016754|2=Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers}}</ref>
*2026
* '''2027''' – [[super-prime]], [[safe prime]]<ref name=":3">{{Cite OEIS|A005385|Safe primes}}</ref>
* '''2027''' – [[super-prime]], [[safe prime]]<ref name=":3">{{Cite OEIS|A005385|Safe primes}}</ref>
*2028
* '''2029''' – member of the [[Mian–Chowla sequence]]<ref name=":4">{{Cite OEIS|A005282|Mian-Chowla sequence}}</ref>
* '''2029''' – member of the [[Mian–Chowla sequence]]<ref name=":4">{{Cite OEIS|A005282|Mian-Chowla sequence}}</ref>
* '''2030''' = 21<sup>2</sup> + 22<sup>2</sup> + 23<sup>2</sup> + 24<sup>2</sup> = 25<sup>2</sup> + 26<sup>2</sup> + 27<sup>2</sup>
* '''2030''' = 21<sup>2</sup> + 22<sup>2</sup> + 23<sup>2</sup> + 24<sup>2</sup> = 25<sup>2</sup> + 26<sup>2</sup> + 27<sup>2</sup>
* '''2031''' – [[centered pentagonal number]]<ref name=":5">{{Cite OEIS|A005891|Centered pentagonal numbers}}</ref>
* '''2031''' – [[centered pentagonal number]]<ref name=":5">{{Cite OEIS|A005891|Centered pentagonal numbers}}</ref>
*2032
*2033
*2034
*2035
*2036
*2037
*2038
* '''2039''' – [[Sophie Germain prime]], [[safe prime]]<ref name=":3" />
* '''2039''' – [[Sophie Germain prime]], [[safe prime]]<ref name=":3" />
*2040
*2041
*2042
*2043
*2044
* '''2045''' – number of [[partially ordered set]] with 7 unlabeled elements<ref>{{cite OEIS|A000112|Number of partially ordered sets (posets) with n unlabeled elements}}</ref>
* '''2045''' – number of [[partially ordered set]] with 7 unlabeled elements<ref>{{cite OEIS|A000112|Number of partially ordered sets (posets) with n unlabeled elements}}</ref>
*2046
* '''2047''' – [[super-Poulet number]],<ref name=":6">{{Cite OEIS|A050217|Super-Poulet numbers}}</ref> [[Woodall number]],<ref>{{Cite OEIS|A003261|Woodall numbers}}</ref> [[decagonal number]],<ref name=":7">{{Cite OEIS|A001107|10-gonal (or decagonal) numbers}}</ref> a [[centered octahedral number]],<ref name="ReferenceA">{{cite OEIS|A001845|Centered octahedral numbers (crystal ball sequence for cubic lattice)}}</ref> 2047 = 2<sup>11</sup> - 1 = 23 × 89 and is the first [[Mersenne number]] that is composite for a prime exponent
* '''2047''' – [[super-Poulet number]],<ref name=":6">{{Cite OEIS|A050217|Super-Poulet numbers}}</ref> [[Woodall number]],<ref>{{Cite OEIS|A003261|Woodall numbers}}</ref> [[decagonal number]],<ref name=":7">{{Cite OEIS|A001107|10-gonal (or decagonal) numbers}}</ref> a [[centered octahedral number]],<ref name="ReferenceA">{{cite OEIS|A001845|Centered octahedral numbers (crystal ball sequence for cubic lattice)}}</ref> 2047 = 2<sup>11</sup> - 1 = 23 × 89 and is the first [[Mersenne number]] that is composite for a prime exponent
* '''2048''' = [[power of two|2<sup>11</sup>]]
* '''2048''' = [[power of two|2<sup>11</sup>]]
*2049
*2050
*2051
*2052
* '''2053''' – [[star number]]
* '''2053''' – [[star number]]
*2054
*2055
* '''2056''' – [[magic constant]] of ''n'' × ''n'' normal [[magic square]] and [[Eight queens puzzle|''n''-queens problem]] for ''n'' = 16
* '''2056''' – [[magic constant]] of ''n'' × ''n'' normal [[magic square]] and [[Eight queens puzzle|''n''-queens problem]] for ''n'' = 16
*2057
*2058
*2059
* '''2060''' – sum of the [[totient function]] for the first 82 integers
* '''2060''' – sum of the [[totient function]] for the first 82 integers
*2061
*2062
* '''2063''' – [[Sophie Germain prime]], [[safe prime]],<ref name=":3" /> [[super-prime]]
* '''2063''' – [[Sophie Germain prime]], [[safe prime]],<ref name=":3" /> [[super-prime]]
*2064
*2065
*2066
*2067
* '''2068''' – number of 16-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed<ref>{{cite OEIS|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}}</ref>
* '''2068''' – number of 16-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed<ref>{{cite OEIS|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}}</ref>
* '''2069''' – [[Sophie Germain prime]]
* '''2069''' – [[Sophie Germain prime]]
* '''2070''' – [[pronic number]]<ref name=A002378>{{Cite OEIS|A002378|Oblong (or promic, pronic, or heteromecic) numbers}}</ref>
* '''2070''' – [[pronic number]]<ref name=A002378>{{Cite OEIS|A002378|Oblong (or promic, pronic, or heteromecic) numbers}}</ref>
*2071
*2072
*2073
*2074
*2075
*2076
*2077
*2078
*2079
* '''2080''' – triangular number
* '''2080''' – triangular number
* '''2081''' – [[super-prime]]
* '''2081''' – [[super-prime]]
*2082
*2083
*2084
*2085
*2086
*2087
*2088
*2089
*2090
*2091
*2092
* '''2093''' – Mertens function zero
* '''2093''' – Mertens function zero
*2094
* '''2095''' – Mertens function zero
* '''2095''' – Mertens function zero
* '''2096''' – Mertens function zero
* '''2096''' – Mertens function zero
* '''2097''' – Mertens function zero
* '''2097''' – Mertens function zero
*2098
* '''2099''' – Mertens function zero, [[super-prime]], [[safe prime]],<ref name=":3" /> [[highly cototient number]]<ref name=":9">{{Cite OEIS|A100827|Highly cototient numbers}}</ref>
* '''2099''' – Mertens function zero, [[super-prime]], [[safe prime]],<ref name=":3" /> [[highly cototient number]]<ref name=":9">{{Cite OEIS|A100827|Highly cototient numbers}}</ref>


Revision as of 19:03, 18 May 2024

"2,000" redirects here. For other uses, see 2000 (disambiguation).
See also: millennium, 2000, and Y2K
← 1999 2000 2001 →
Cardinaltwo thousand
Ordinal2000th
(two thousandth)
Factorization24 × 53
Greek numeral,Β´
Roman numeralMM
Unicode symbol(s)MM, mm
Binary111110100002
Ternary22020023
Senary131326
Octal37208
Duodecimal11A812
Hexadecimal7D016
ArmenianՍ
Egyptian hieroglyph𓆽
Look up two thousand in Wiktionary, the free dictionary.

2000 (two thousand) is a natural number following 1999 and preceding 2001.

It is:

Selected numbers in the range 2001–2999

2001 to 2099

2100 to 2199

2200 to 2299

2300 to 2399

2400 to 2499

2500 to 2599

  • 2500 = 502, palindromic in base 7 (102017)
  • 2501 – Mertens function zero
  • 2502 – Mertens function zero
  • 2503 – Friedman prime
  • 2510 – member of the Mian–Chowla sequence[20]
  • 2513 – member of the Padovan sequence[61]
  • 2517 – Mertens function zero
  • 2519 – the smallest number congruent to 1 (mod 2), 2 (mod 3), 3 (mod 4), ..., 9 (mod 10)
  • 2520 – superior highly composite number; smallest number divisible by numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 12; colossally abundant number; Harshad number in several bases. It is also the highest number with more divisors than any number less than double itself (sequence A072938 in the OEIS). Not only it is the 7th (and last) number with more divisors than any number double itself but is also the 7th number that is highly composite and the lowest common multiple of a consecutive set of integers from 1 (sequence A095921 in the OEIS) which is a property the previous number with this pattern of divisors does not have (360). That is, although 360 and 2520 both have more divisors than any number twice themselves, 2520 is the lowest number divisible by both 1 to 9 and 1 to 10, whereas 360 is not the lowest number divisible by 1 to 6 (which 60 is) and is not divisible by 1 to 7 (which 420 is). It is also the 6th and largest highly composite number that is a divisor of every higher highly composite number (sequence A106037 in the OEIS).
  • 2521 – star prime, centered square number[33]
  • 2522 – Mertens function zero
  • 2523 – Mertens function zero
  • 2524 – Mertens function zero
  • 2525 – Mertens function zero
  • 2530 – Mertens function zero, Leyland number[36]
  • 2533 – Mertens function zero
  • 2537 – Mertens function zero
  • 2538 – Mertens function zero
  • 2543 – Sophie Germain prime, sexy prime with 2549
  • 2549 – Sophie Germain prime, super-prime, sexy prime with 2543
  • 2550 – pronic number[28]
  • 2552 – sum of the totient function for the first 91 integers
  • 2556 – triangular number
  • 2567 – Mertens function zero
  • 2568 – Mertens function zero, number of digits in the decimal expansion of 1000!, or the product of all natural numbers from 1 to 1000
  • 2570 – Mertens function zero
  • 2579 – safe prime[19]
  • 2580 – Keith number,[46] forms a column on a telephone or PIN pad
  • 2584 – Fibonacci number,[62] sum of the first 37 primes
  • 2592 – 3-smooth number (25×34)
  • 2596 – sum of the totient function for the first 92 integers

2600 to 2699

2700 to 2799

  • 2701 – triangular number, super-Poulet number[23]
  • 2702 – sum of the totient function for the first 94 integers
  • 2704 = 522
  • 2707 – model number for the concept supersonic airliner Boeing 2707
  • 2719 – super-prime, largest known odd number which cannot be expressed in the form x2 + y2 + 10z2 where x, y and z are integers.[63] In 1997 it was conjectured that this is also the largest such odd number.[64] It is now[when?] known this is true if the generalized Riemann hypothesis is true.[65]
  • 2728 – Kaprekar number[47]
  • 2729 – highly cototient number[29]
  • 2731 – the only Wagstaff prime with four digits,[66] Jacobsthal prime
  • 2736 – octahedral number[48]
  • 2741 – Sophie Germain prime, 400th prime number
  • 2744 = 143, palindromic in base 13 (133113)
  • 2747 – sum of the first 38 primes
  • 2749 – super-prime, cousin prime with 2753
  • 2753 – Sophie Germain prime, Proth prime[32]
  • 2756 – pronic number[28]
  • 2774 – sum of the totient function for the first 95 integers
  • 2775 – triangular number
  • 2780 – member of the Mian–Chowla sequence[20]
  • 2783 – member of a Ruth–Aaron pair with 2784 (first definition)
  • 2784 – member of a Ruth–Aaron pair with 2783 (first definition)
  • 2791 – cuban prime[49]

2800 to 2899

2900 to 2999

Prime numbers

There are 127 prime numbers between 2000 and 3000:[76][77]

2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999

References

  1. ^ Sloane, N. J. A. (ed.). "Sequence A052486 (Achilles numbers - powerful but imperfect: if n = Product(p_i^e_i) then all e_i > 1 (i.e., powerful), but the highest common factor of the e_i is 1, i.e., not a perfect power)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A006933 ('Eban' numbers (the letter 'e' is banned!))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A008537 (Numbers that do not contain the letter 'n'))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A007304 (Sphenic numbers: products of 3 distinct primes))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A022264 (n*(7*n - 1)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A085945 (Number of subsets of {1,2,...,n} with relatively prime elements)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^ Sloane, N. J. A. (ed.). "Sequence A064539 (Numbers n such that 2^n + n^2 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. ^ Sloane, N. J. A. (ed.). "Sequence A001496 (Number of 4 X 4 matrices with nonnegative integer entries and row and column sums equal to n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  9. ^ Sloane, N. J. A. (ed.). "Sequence A000740 (Number of 2n-bead balanced binary necklaces of fundamental period 2n, equivalent to reversed complement)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  10. ^ Sloane, N. J. A. (ed.). "Sequence A056721 (Numbers n such that 8*10^n-1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  11. ^ Sloane, N. J. A. (ed.). "Sequence A001770 (Numbers k such that 5*2^k - 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  12. ^ a b Sloane, N. J. A. (ed.). "Sequence A006972 (Lucas-Carmichael numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  13. ^ Sloane, N. J. A. (ed.). "Sequence A194472 (Erdős-Nicolas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  14. ^ "Can you solve it? 2019 in numbers". the Guardian. 2018-12-31. Retrieved 2021-09-19.
  15. ^ Sloane, N. J. A. (ed.). "Sequence A294685 (non-isomorphic colorings of a toroidal n X k grid using exactly three colors under translational symmetry)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  16. ^ Sloane, N. J. A. (ed.). "Sequence A141769 (Beginning of a run of 4 consecutive Niven (or Harshad) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  17. ^ Sloane, N. J. A. (ed.). "Sequence A063416 (Multiples of 7 whose sum of digits is equal to 7)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  18. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A016754 (Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  19. ^ a b c d e f g h i j k Sloane, N. J. A. (ed.). "Sequence A005385 (Safe primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  20. ^ a b c d e f Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  21. ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A005891 (Centered pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  22. ^ 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.
  23. ^ a b Sloane, N. J. A. (ed.). "Sequence A050217 (Super-Poulet numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  24. ^ Sloane, N. J. A. (ed.). "Sequence A003261 (Woodall numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  25. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A001107 (10-gonal (or decagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  26. ^ a b Sloane, N. J. A. (ed.). "Sequence A001845 (Centered octahedral numbers (crystal ball sequence for cubic lattice))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  27. ^ 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.
  28. ^ a b c d e f g h i j Sloane, N. J. A. (ed.). "Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  29. ^ a b c Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  30. ^ a b c d Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  31. ^ a b c Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  32. ^ a b c Sloane, N. J. A. (ed.). "Sequence A080076 (Proth primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  33. ^ a b c d e f g Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  34. ^ Sloane, N. J. A. (ed.). "Sequence A000957 (Fine's sequence (or Fine numbers): number of relations of valence >= 1 on an n-set; also number of ordered rooted trees with n edges having root of even degree)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  35. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A001106 (9-gonal (or enneagonal or nonagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  36. ^ a b Sloane, N. J. A. (ed.). "Sequence A076980 (Leyland numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  37. ^ Sloane, N. J. A. (ed.). "Sequence A002411 (Pentagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  38. ^ Sloane, N. J. A. (ed.). "Sequence A008918 (Numbers n such that 4*n = (n written backwards))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-14.
  39. ^ Sloane, N. J. A. (ed.). "Sequence A001190 (Wedderburn-Etherington numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  40. ^ Mackenzie, Dana (2018). "2184: An Absurd (and Adsurd) Tale". Integers. 18.
  41. ^ Sloane, N. J. A. (ed.). "Sequence A014575 (Vampire numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  42. ^ a b Sloane, N. J. A. (ed.). "Sequence A082897 (Perfect totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  43. ^ Sloane, N. J. A. (ed.). "Sequence A001006 (Motzkin numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  44. ^ a b Sloane, N. J. A. (ed.). "Sequence A005231 (Odd abundant numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  45. ^ Sloane, N. J. A. (ed.). "Sequence A005479 (Prime Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  46. ^ a b Sloane, N. J. A. (ed.). "Sequence A007629 (Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  47. ^ a b Sloane, N. J. A. (ed.). "Sequence A006886 (Kaprekar numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  48. ^ a b Sloane, N. J. A. (ed.). "Sequence A005900 (Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  49. ^ a b c Sloane, N. J. A. (ed.). "Sequence A002407 (Cuban primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  50. ^ a b c d e Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  51. ^ a b c Cite error: The named reference :1 was invoked but never defined (see the help page).
  52. ^ Sloane, N. J. A. (ed.). "Sequence A002110 (Primorial numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  53. ^ "The Small Groups library". Archived from the original on 2007-02-04. Retrieved 2008-01-22..
  54. ^ Sloane, N. J. A. (ed.). "Sequence A005898 (Centered cube numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  55. ^ Sloane, N. J. A. (ed.). "Sequence A069151 (Concatenations of consecutive primes, starting with 2, that are also prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  56. ^ Sloane, N. J. A. (ed.). "Sequence A002104 (Logarithmic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  57. ^ Sloane, N. J. A. (ed.). "Sequence A000129 (Pell numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  58. ^ a b Sloane, N. J. A. (ed.). "Sequence A002997 (Carmichael numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  59. ^ 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.
  60. ^ 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.
  61. ^ Sloane, N. J. A. (ed.). "Sequence A000931 (Padovan sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  62. ^ Sloane, N. J. A. (ed.). "Sequence A000045 (Fibonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  63. ^ "Odd numbers that are not of the form x^2+y^2+10*z^2.". The Online Encyclopedia of Integer Sequences. The OEIS Foundation, Inc. Retrieved 13 November 2012.
  64. ^ Ono, Ken (1997). "Ramanujan, taxicabs, birthdates, zipcodes and twists" (PDF). American Mathematical Monthly. 104 (10): 912–917. CiteSeerX 10.1.1.514.8070. doi:10.2307/2974471. JSTOR 2974471. Archived from the original (PDF) on 15 October 2015. Retrieved 11 November 2012.
  65. ^ Ono, Ken; K Soundararajan (1997). "Ramanujan's ternary quadratic forms" (PDF). Inventiones Mathematicae. 130 (3): 415–454. Bibcode:1997InMat.130..415O. CiteSeerX 10.1.1.585.8840. doi:10.1007/s002220050191. S2CID 122314044. Archived from the original (PDF) on 18 July 2019. Retrieved 12 November 2012.
  66. ^ Sloane, N. J. A. (ed.). "Sequence A000979 (Wagstaff primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  67. ^ Sloane, N. J. A. (ed.). "Sequence A001792 (a(n) = (n+2)*2^(n-1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  68. ^ Sloane, N. J. A. (ed.). "Sequence A144974 (Centered heptagonal prime numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  69. ^ Sloane, N. J. A. (ed.). "Sequence A000078 (Tetranacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  70. ^ Pandharipande, Rahul (1998), "Rational curves on hypersurfaces (after A. Givental)", Astérisque, 1997/98 (252): 307–340, arXiv:math/9806133, Bibcode:1998math......6133P, MR 1685628
  71. ^ Sloane, N. J. A. (ed.). "Sequence A002559 (Markoff (or Markov) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  72. ^ 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.
  73. ^ Sloane, N. J. A. (ed.). "Sequence A001599 (Harmonic or Ore numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  74. ^ Sloane, N. J. A. (ed.). "Sequence A000014 (Number of series-reduced trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  75. ^ Sloane, N. J. A. (ed.). "Sequence A195163 (1000-gonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-13.
  76. ^ Sloane, N. J. A. (ed.). "Sequence A038823 (Number of primes between n*1000 and (n+1)*1000)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  77. ^ Stein, William A. (10 February 2017). "The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture". wstein.org. Retrieved 6 February 2021.
Retrieved from "https://en.wikipedia.org/w/index.php?title=2000_(number)&oldid=1224490892"