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This article provides a list of integer sequences in the On-Line Encyclopedia of Integer Sequences that have their own Wikipedia entries. = \frac = \prod\limits_^\frac \qquad for ''n'' ≥ 0. |- | || Bell number || 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147 || The number of partitions of a set with ''n'' elements |- | || Euler number || 1, 1, 1, 2, 5, 16, 61, 272, 1385, 7936 || The number of linear extensions of the "zig-zag" poset |- | || 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 ''n'' cuts |- | || Pell number || 0, 1, 2, 5, 12, 29, 70, 169, 408, 985 || ''a''(0) = 0, ''a''(1) = 1; for ''n'' > 1, ''a''(''n'') = 2''a''(''n'' − 1) + ''a''(''n'' − 2) |- | || Factorial || 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880 || ''n''! = 1·2·3·4·...·n |- | || Triangular number || 0, 1, 3, 6, 10, 15, 21, 28, 36, 45 || ''a''(''n'') = ''C''(''n'' + 1, 2) = ''n''(''n'' + 1)/2 = 0 + 1 + 2 + ... + ''n'' |- | || Tetrahedral number || 0, 1, 4, 10, 20, 35, 56, 84, 120, 165 || The sum of the first ''n'' triangular numbers |- | || Square pyramidal number || 0, 1, 5, 14, 30, 55, 91, 140, 204, 285 || (n(n+1)(2n+1)) / 6 The number of stacked spheres in a pyramid with a square base |- | || Perfect number || 6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128 || ''n'' is equal to the sum of the proper divisors of ''n'' |- | || Mersenne prime || 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111 || 2''p'' − 1 if p is a prime |- | || Stella octangula number || 0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990, 2651, 3444, 4381, ...|| Stella octangula numbers: n *(2 *n''2'' - 1). |- | || Landau's function || 1, 1, 2, 3, 4, 6, 6, 12, 15, 20 || The largest order of permutation of ''n'' elements |- | || Decimal expansion of Pi || 3, 1, 4, 1, 5, 9, 2, 6, 5, 3 || |- | || Padovan sequence || 1, 1, 1, 2, 2, 3, 4, 5, 7, 9 || ''P''(0) = ''P''(1) = ''P''(2) = 1, ''P''(''n'') = ''P''(''n''−2)+''P''(''n''−3) |- | || Euclid–Mullin sequence || 2, 3, 7, 43, 13, 53, 5, 6221671, 38709183810571, 139 || ''a''(1) = 2, ''a''(''n''+1) is smallest prime factor of ''a''(1)''a''(2)''...a''(''n'')+1. |- | || Lucky number || 1, 3, 7, 9, 13, 15, 21, 25, 31, 33 || A natural number in a set that is filtered by a sieve |- | || Motzkin number || 1, 1, 2, 4, 9, 21, 51, 127, 323, 835 || The number of ways of drawing any number of nonintersecting chords joining ''n'' (labeled) points on a circle |- | || Jacobsthal number || 0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341 || ''a''(''n'') = ''a''(''n'' − 1) + 2''a''(''n'' − 2), with ''a''(0) = 0, ''a''(1) = 1 |- | || sequence of Aliquot sums s(n) || 0, 1, 1, 3, 1, 6, 1, 7, 4, 8 || s(n) is the sum of the proper divisors of the integer n |- | || Decimal expansion of e (mathematical constant) || 2, 7, 1, 8, 2, 8, 1, 8, 2, 8 || |- | || Wedderburn–Etherington number || 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 n endpoints (and 2''n'' − 1 nodes in all) |- | || Semiprime || 4, 6, 9, 10, 14, 15, 21, 22, 25, 26 || Products of two primes |- | || Golomb sequence || 1, 2, 2, 3, 3, 4, 4, 4, 5, 5 || ''a''(''n'') is the number of times ''n'' occurs, starting with ''a''(1) = 1 |- | || Perrin number || 3, 0, 2, 3, 2, 5, 5, 7, 10, 12 || ''P''(0) = 3, ''P''(1) = 0, ''P''(2) = 2; ''P''(''n'') = ''P''(''n''−2) + ''P''(''n''−3) for ''n'' > 2 |- | || Euler–Mascheroni constant || 5, 7, 7, 2, 1, 5, 6, 6, 4, 9 || |- | || Decimal expansion of the golden ratio || 1, 6, 1, 8, 0, 3, 3, 9, 8, 8 || |- | || Cullen number || 1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153, 106497 || n 2n + 1 |- | || Primorial || 1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870 || The product of first ''n'' primes |- | || Palindromic number || 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 || A number that remains the same when its digits are reversed |- | || Highly composite number || 1, 2, 4, 6, 12, 24, 36, 48, 60, 120 || A positive integer with more divisors than any smaller positive integer |- | || Decimal expansion of square root of 2 || 1, 4, 1, 4, 2, 1, 3, 5, 6, 2 || |- | || Superior highly composite number || 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720 || A positive integer ''n'' for which there is an ''e''>0 such that ''d''(''n'')/''ne'' ≥ ''d''(''k'')/''ke'' for all ''k''>1 |- | || Pronic number || 0, 2, 6, 12, 20, 30, 42, 56, 72, 90 || ''n''(''n''+1) |- | || Composite number || 4, 6, 8, 9, 10, 12, 14, 15, 16, 18 || The numbers ''n'' of the form ''xy'' for ''x'' > 1 and ''y'' > 1 |- | || Ulam number || 1, 2, 3, 4, 6, 8, 11, 13, 16, 18 || ''a''(1) = 1; ''a''(2) = 2; for ''n''>2, ''a''(''n'') = least number > ''a''(''n''-1) which is a unique sum of two distinct earlier terms; semiperfect |- | || Carmichael number || 561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341 || Composite numbers ''n'' such that ''a''(''n''−1) == 1 (mod ''n'') if ''a'' is prime to ''n'' |- | || Woodall number || 1, 7, 23, 63, 159, 383, 895, 2047, 4607 || n 2n - 1 |- | || Permutable prime || 2, 3, 5, 7, 11, 13, 17, 31, 37, 71 || The numbers for which every permutation of digits is a prime |- | || 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 ''n'' |- | || Deficient number || 1, 2, 3, 4, 5, 7, 8, 9, 10, 11 || The numbers ''n'' such that σ(''n'') < 2''n'' |- | || Abundant number || 12, 18, 20, 24, 30, 36, 40, 42, 48, 54 || The sum of divisors of ''n'' exceeds 2''n'' |- | || Look-and-say sequence || 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, 13211311123113112211, || A = 'frequency' followed by 'digit'-indication |- | || 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 |- | || Fortunate number || 3, 5, 7, 13, 23, 17, 19, 23, 37, 61 || The smallest integer m > 1 such that pn# + m is a prime number, where the primorial pn# is the product of the first n prime numbers |- | || Harshad numbers 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) |- | || Sophie Germain prime || 2, 3, 5, 11, 23, 29, 41, 53, 83, 89 || A prime number ''p'' such that 2''p''+1 is also prime |- | || Semiperfect number || 6, 12, 18, 20, 24, 28, 30, 36, 40, 42 || A natural number ''n'' that is equal to the sum of all or some of its proper divisors |- | || Weird number || 70, 836, 4030, 5830, 7192, 7912, 9272, 10430, 10570, 10792 || A natural number that is abundant but not semiperfect |- | || Farey sequence numerators || 0, 1, 0, 1, 1, 0, 1, 1, 2, 1 || |- | || Farey sequence denominators || 1, 1, 1, 2, 1, 1, 3, 2, 3, 1 || |- | || Euclid number || 2, 3, 7, 31, 211, 2311, 30031, 510511, 9699691, 223092871 || 1 + product of first ''n'' consecutive primes |- | || Kaprekar number || 1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728 || ''X''² = ''Abn'' + ''B'', where 0 < ''B'' < ''bn'' ''X'' = ''A'' + ''B'' |- | || Sphenic number || 30, 42, 66, 70, 78, 102, 105, 110, 114, 130 || Products of 3 distinct primes |- | || Pascal's triangle || 1, 1, 1, 1, 2, 1, 1, 3, 3, 1 || Pascal's triangle read by rows |- | || Happy number || 1, 7, 10, 13, 19, 23, 28, 31, 32, 44 || The numbers whose trajectory under iteration of sum of squares of digits map includes 1 |- | || Prouhet–Thue–Morse constant || 0, 1, 1, 0, 1, 0, 0, 1, 1, 0 || consists only of composite numbers |- | || Riesel number || 509203, 762701, 777149, 790841, 992077 || Odd ''k'' for which consists only of composite numbers |- | || Baum–Sweet sequence || 1, 1, 0, 1, 1, 0, 0, 1, 0, 1 || ''a''(''n'') = 1 if binary representation of ''n'' contains no block of consecutive zeros of odd length; otherwise ''a''(''n'') = 0 |- | || Juggler sequence || 0, 1, 1, 5, 2, 11, 2, 18, 2, 27 || If ''n'' mod 2 = 0 then floor(√''n'') else floor(''n''3/2) |- | || Highly totient number || 1, 2, 4, 8, 12, 24, 48, 72, 144, 240 || Each number ''k'' on this list has more solutions to the equation φ(''x'') = ''k'' than any preceding ''k'' |- | || Decimal expansion of Chaitin's constant || 0, 0, 7, 8, 7, 4, 9, 9, 6, 9 || |- | || Ramanujan prime || 2, 11, 17, 29, 41, 47, 59, 67 || The ''n''th Ramanujan prime is the least integer ''Rn'' for which ≥ ''n'', for all ''x'' ≥ ''Rn''. |- | || Euler number || 1, 0, −1, 0, 5, 0, −61, 0, 1385, 0 || |} ==References== * (OEIS core sequences ) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「List of OEIS sequences」の詳細全文を読む スポンサード リンク
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