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| This article provides a list of [[integer sequence]]s in the [[On-Line Encyclopedia of Integer Sequences]] that have their own [[Wikipedia]] entries.
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| {|class="wikitable sortable"
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| ! OEIS link !! Name !! First elements !! Short description
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| | {{OEIS link|A000027}} || [[Natural number]] || 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 || The natural numbers
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| | {{OEIS link|A000032}} || [[Lucas number]] || 2, 1, 3, 4, 7, 11, 18, 29, 47, 76 || ''L''(''n'') = ''L''(''n'' − 1) + ''L''(''n'' − 2)
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| | {{OEIS link|A000040}} || [[Prime number]] || 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 || The prime numbers
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| | {{OEIS link|A000045}} || [[Fibonacci number]] || 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 || ''F''(''n'') = ''F''(''n'' − 1) + F(''n'' − 2) with ''F''(0) = 0 and ''F''(1) = 1
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| | {{OEIS link|A000058}} || [[Sylvester's sequence]] || 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443 || ''a''(''n'' + 1) = ''a''(''n'')<sup>2</sup> − ''a''(''n'') + 1, with ''a''(0) = 2
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| | {{OEIS link|A000108}} || [[Catalan number]] || 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} \qquad</math> for ''n'' ≥ 0.
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| | {{OEIS link|A000110}} || [[Bell number]] || 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147 || The number of partitions of a set with ''n'' elements
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| | {{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 ''n'' cuts
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| | {{OEIS link|A000129}} || [[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)
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| | {{OEIS link|A000142}} || [[Factorial]] || 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880 || ''n''! = 1·2·3·4·...·n
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| | {{OEIS link|A000217}} || [[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''
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| | {{OEIS link|A000292}} || [[Tetrahedral number]] || 0, 1, 4, 10, 20, 35, 56, 84, 120, 165 || The sum of the first ''n'' triangular numbers
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| | {{OEIS link|A000330}} || [[Square pyramidal number]] || 0, 1, 5, 14, 30, 55, 91, 140, 204, 285 || (n(n+1)(2n+1)) / 6
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| The number of stacked spheres in a pyramid with a square base
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| | {{OEIS link|A000396}} || [[Perfect number]] || 6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128 || ''n'' is equal to the sum of the proper divisors of ''n''
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| | {{OEIS link|A000668}} || [[Mersenne prime]] || 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111 || 2<sup>''p''</sup> − 1 if p is a prime
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| | {{OEIS link|A000793}} || [[Landau's function]] || 1, 1, 2, 3, 4, 6, 6, 12, 15, 20 || The largest order of permutation of ''n'' elements
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| | {{OEIS link|A000796}} || Decimal expansion of [[Pi]] || 3, 1, 4, 1, 5, 9, 2, 6, 5, 3 ||
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| | {{OEIS link|A000931}} || [[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)
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| | {{OEIS link|A000945}} || [[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.
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| | {{OEIS link|A000959}} || [[Lucky number]] || 1, 3, 7, 9, 13, 15, 21, 25, 31, 33 || A natural number in a set that is filtered by a sieve
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| | {{OEIS link|A001006}} || [[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
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| | {{OEIS link|A001045}} || [[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
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| | {{OEIS link|A001113}} || Decimal expansion of [[e (mathematical constant)]] || 2, 7, 1, 8, 2, 8, 1, 8, 2, 8 ||
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| | {{OEIS link|A001190}} || [[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)
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| | {{OEIS link|A001358}} || [[Semiprime]] || 4, 6, 9, 10, 14, 15, 21, 22, 25, 26 || Products of two primes
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| | {{OEIS link|A001462}} || [[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
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| | {{OEIS link|A001608}} || [[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
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| | {{OEIS link|A001620}} || [[Euler–Mascheroni constant]] || 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>
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| | {{OEIS link|A001622}} || Decimal expansion of the [[golden ratio]] || 1, 6, 1, 8, 0, 3, 3, 9, 8, 8 || <math>\varphi = \frac{1+\sqrt{5}}{2} = 1.61803\,39887\ldots.</math>
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| | {{OEIS link|A002110}} || [[Primorial]] || 1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870 || The product of first ''n'' primes
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| | {{OEIS link|A002113}} || [[Palindromic number]] || 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 || A number that remains the same when its digits are reversed
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| | {{OEIS link|A002182}} || [[Highly composite number]] || 1, 2, 4, 6, 12, 24, 36, 48, 60, 120 || A positive integer with more divisors than any smaller positive integer
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| | {{OEIS link|A002193}} || Decimal expansion of [[square root of 2]] || 1, 4, 1, 4, 2, 1, 3, 5, 6, 2 ||
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| | {{OEIS link|A002201}} || [[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'')/''n<sup>e</sup>'' ≥ ''d''(''k'')/''k<sup>e</sup>'' for all ''k''>1
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| | {{OEIS link|A002378}} || [[Pronic number]] || 0, 2, 6, 12, 20, 30, 42, 56, 72, 90 || ''n''(''n''+1)
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| | {{OEIS link|A002808}} || [[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
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| | {{OEIS link|A002858}} || [[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
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| | {{OEIS link|A002997}} || [[Carmichael number]] || 561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341 || Composite numbers ''n'' such that ''a''<sup>(''n''−1)</sup> == 1 (mod ''n'') if ''a'' is prime to ''n''
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| | {{OEIS link|A003459}} || [[Permutable prime]] || 2, 3, 5, 7, 11, 13, 17, 31, 37, 71 || The numbers for which every permutation of digits is a prime
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| | {{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 ''n''
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| | {{OEIS link|A005100}} || [[Deficient number]] || 1, 2, 3, 4, 5, 7, 8, 9, 10, 11 || The numbers ''n'' such that σ(''n'') < 2''n''
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| | {{OEIS link|A005101}} || [[Abundant number]] || 12, 18, 20, 24, 30, 36, 40, 42, 48, 54 || The sum of divisors of ''n'' exceeds 2''n''
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| | {{OEIS link|A005150}} || [[Look-and-say sequence]] || 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, 13211311123113112211, || A = 'frequency' followed by 'digit'-indication
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| | {{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
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| | {{OEIS link|A005235}} || [[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
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| | {{OEIS link|A005384}} || [[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
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| | {{OEIS link|A005835}} || [[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
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| | {{OEIS link|A006037}} || [[Weird number]] || 70, 836, 4030, 5830, 7192, 7912, 9272, 10430, 10570, 10792 || A natural number that is abundant but not semiperfect
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| | {{OEIS link|A006842}} || [[Farey sequence]] numerators || 0, 1, 0, 1, 1, 0, 1, 1, 2, 1 ||
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| | {{OEIS link|A006843}} || [[Farey sequence]] denominators || 1, 1, 1, 2, 1, 1, 3, 2, 3, 1 ||
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| | {{OEIS link|A006862}} || [[Euclid number]] || 2, 3, 7, 31, 211, 2311, 30031, 510511, 9699691, 223092871 || 1 + product of first ''n'' consecutive primes
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| | {{OEIS link|A006886}} || [[Kaprekar number]] || 1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728 || ''X''² = ''Ab<sup>n</sup>'' + ''B'', where 0 < ''B'' < ''b<sup>n</sup>'' ''X'' = ''A'' + ''B''
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| | {{OEIS link|A007304}} || [[Sphenic number]] || 30, 42, 66, 70, 78, 102, 105, 110, 114, 130 || Products of 3 distinct primes
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| | {{OEIS link|A007318}} || [[Pascal's triangle]] || 1, 1, 1, 1, 2, 1, 1, 3, 3, 1 || Pascal's triangle read by rows
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| | {{OEIS link|A007770}} || [[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
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| | {{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>
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| | {{OEIS link|A014080}} || [[Factorion]] || 1, 2, 145, 40585 || A natural number that equals the sum of the factorials of its decimal digits
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| | {{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
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| | {{OEIS link|A016114}} || [[Circular prime]] || 2, 3, 5, 7, 11, 13, 17, 37, 79, 113 || The numbers which remain prime under cyclic shifts of digits
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| | {{OEIS link|A019279}} || [[Superperfect number]] || 2, 4, 16, 64, 4096, 65536, 262144, 1073741824, 1152921504606846976, 309485009821345068724781056 || <math>\sigma^2(n)=\sigma(\sigma(n))=2n\, ,</math>
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| | {{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
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| | {{OEIS link|A033307}} || Decimal expansion of [[Champernowne constant]] || 1, 2, 3, 4, 5, 6, 7, 8, 9, 1 || formed by concatenating the positive integers
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| | {{OEIS link|A035513}} || [[Wythoff array]] || 1, 2, 4, 3, 7, 6, 5, 11, 10, 9 || A matrix of integers derived from the Fibonacci sequence
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| | {{OEIS link|A036262}} || [[Gilbreath's conjecture]] || 2, 1, 3, 1, 2, 5, 1, 0, 2, 7 || Triangle of numbers arising from Gilbreath's conjecture
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| | {{OEIS link|A037274}} || [[Home prime]] || 1, 2, 3, 211, 5, 23, 7, 3331113965338635107, 311, 773 || For ''n'' ≥ 2, ''a''(''n'') = the prime that is finally reached when you start with ''n'', concatenate its prime factors (A037276) and repeat until a prime is reached; ''a''(''n'') = −1 if no prime is ever reached
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| | {{OEIS link|A046075}} || [[Undulating number]] || 101, 121, 131, 141, 151, 161, 171, 181, 191, 202 || A number that has the digit form ''ababab''
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| | {{OEIS link|A050278}} || [[Pandigital number]] || 1023456789, 1023456798, 1023456879, 1023456897, 1023456978, 1023456987, 1023457689, 1023457698, 1023457869, 1023457896 || Numbers containing the digits 0-9 such that each digit appears exactly once
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| | {{OEIS link|A052486}} || [[Achilles number]] || 72, 108, 200, 288, 392, 432, 500, 648, 675, 800 || Powerful but imperfect
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| | {{OEIS link|A060006}} || Decimal expansion of [[Pisot–Vijayaraghavan number]] || 1, 3, 2, 4, 7, 1, 7, 9, 5, 7 || real root of ''x''<sup>3</sup>−''x''−1
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| | {{OEIS link|A076336}} || [[Sierpinski number]] || 78557, 271129, 271577, 322523, 327739, 482719, 575041, 603713, 903983, 934909 || Odd ''k'' for which <math>\left\{\,k 2^n + 1 : n \in\mathbb{N}\,\right\}</math> consists only of composite numbers
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| | {{OEIS link|A076337}} || [[Riesel number]] || 509203 || ''k'' such that <math>\left\{\,k 2^n - 1 : n \in\mathbb{N}\,\right\}</math> is composite for all ''n''
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| | {{OEIS link|A086747}} || [[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
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| | {{OEIS link|A094683}} || [[Juggler sequence]] || 0, 1, 1, 5, 2, 11, 2, 18, 2, 27 || If ''n'' mod 2 = 0 then floor(√''n'') else floor(''n''<sup>3/2</sup>)
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| | {{OEIS link|A097942}} || [[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''
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| | {{OEIS link|A100264}} || Decimal expansion of [[Chaitin's constant]] || 0, 0, 7, 8, 7, 4, 9, 9, 6, 9 ||
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| | {{OEIS link|A122045}} || [[Euler number]] || 1, 0, −1, 0, 5, 0, -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>
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| | {{OEIS link|A018226}} || [[Magic number (physics)]] || 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.
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| | {{OEIS link|A104272}} || [[Ramanujan prime]] || 2, 11, 17, 29, 41, 47, 59, 67 || The ''n''th Ramanujan prime is the least integer ''R<sub>n</sub>'' for which <math>\pi(x) - \pi(x/2)</math> ≥ ''n'', for all ''x'' ≥ ''R<sub>n</sub>''.
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| |}
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| ==References==
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| * [http://oeis.org/wiki/Index_to_OEIS:_Section_Cor#core OEIS core sequences]
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| ==External links== | |
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| * [http://oeis.org/wiki/Index_to_OEIS Index to OEIS]
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| {{Series (mathematics)}}
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| [[Category:Arithmetic functions]]
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| [[Category:Integer sequences]]
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| [[Category:Number-related lists]]
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| {{DEFAULTSORT:OEIS sequences}}
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