OEIS link | Proper name | Starting time elements | Short clarification |
A000002 | Kolakoski sequence | {1, 2, 2, i, one, 2, 1, two, two, 1, ...} | The n thursday term describes the length of the n th run |
A000010 | Euler's totient function φ(n) | {1, 1, two, 2, four, 2, 6, 4, half-dozen, 4, ...} | φ(due north) is the number of positive integers not greater than n that are coprime with north . |
A000032 | Lucas numbers 50(due north) | {2, 1, 3, 4, 7, 11, 18, 29, 47, 76, ...} | L(n) = L(north − 1) + L(n − two) for northward ≥ 2, with 50(0) = ii and Fifty(1) = i. |
A000040 | Prime numbers p n | {two, three, 5, 7, 11, 13, 17, 19, 23, 29, ...} | The prime number numbers p n , with n ≥ ane. A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. |
A000041 | Division numbers P northward | {1, one, 2, iii, 5, 7, 11, 15, 22, 30, 42, ...} | The partition numbers, number of additive breakdowns of north. |
A000045 | Fibonacci numbers F(north) | {0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...} | F(due north) = F(n − 1) + F(n − 2) for n ≥ ii, with F(0) = 0 and F(one) = 1. |
A000058 | Sylvester's sequence | {2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443, ...} | a(n + i) = a(n)⋅a(n − 1)⋅ ⋯ ⋅a(0) + 1 = a(n)2 − a(n) + 1 for n ≥ 1, with a(0) = ii. |
A000073 | Tribonacci numbers | {0, one, 1, ii, iv, 7, xiii, 24, 44, 81, ...} | T(n) = T(north − 1) + T(n − two) + T(due north − 3) for north ≥ three, with T(0) = 0 and T(ane) = T(2) = 1. |
A000079 | Powers of 2 | {1, 2, 4, eight, 16, 32, 64, 128, 256, 512, 1024, ...} | Powers of two: two n for n ≥ 0 |
A000105 | Polyominoes | {1, ane, 1, 2, five, 12, 35, 108, 369, ...} | The number of gratis polyominoes with n cells. |
A000108 | Catalan numbers C n | {1, i, 2, five, 14, 42, 132, 429, 1430, 4862, ...} | |
A000110 | Bell numbers B northward | {1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, ...} | B northward is the number of partitions of a prepare with northward elements. |
A000111 | Euler zigzag numbers E n | {1, 1, 1, ii, 5, 16, 61, 272, 1385, 7936, ...} | East n is the number of linear extensions of the "zig-zag" poset. |
A000124 | Lazy caterer's sequence | {1, ii, iv, seven, 11, 16, 22, 29, 37, 46, ...} | The maximal number of pieces formed when slicing a pancake with n cuts. |
A000129 | Pell numbers P n | {0, ane, 2, 5, 12, 29, seventy, 169, 408, 985, ...} | a(n) = 2a(n − ane) + a(n − 2) for n ≥ 2, with a(0) = 0, a(one) = ane. |
A000142 | Factorials northward! | {1, one, two, 6, 24, 120, 720, 5040, 40320, 362880, ...} | n! = one⋅2⋅3⋅iv⋅ ⋯ ⋅due north for due north ≥ one, with 0! = 1 (empty product). |
A000166 | Derangements | {1, 0, one, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, 14684570, 176214841, ...} | Number of permutations of northward elements with no stock-still points. |
A000203 | Divisor function σ(n) | {1, 3, 4, 7, 6, 12, 8, 15, xiii, eighteen, 12, 28, ...} | σ(north) := σ 1(n) is the sum of divisors of a positive integer n . |
A000215 | Fermat numbers F n | {3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, 340282366920938463463374607431768211457, ...} | F northward = ii 2 northward + i for northward ≥ 0. |
A000238 | Polytrees | {ane, 1, three, eight, 27, 91, 350, 1376, 5743, 24635, 108968, ...} | Number of oriented trees with n nodes. |
A000396 | Perfect numbers | {6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128, ...} | n is equal to the sum s(due north) = σ(north) − n of the proper divisors of due north . |
A000594 | Ramanujan tau part | {1,−24,252,−1472,4830,−6048,−16744,84480,−113643...} | Values of the Ramanujan tau role, τ(n) at due north = 1, 2, 3, ... |
A000793 | Landau's function | {i, one, 2, 3, 4, 6, half-dozen, 12, 15, twenty, ...} | The largest lodge of permutation of n elements. |
A000930 | Narayana'due south cows | {1, 1, 1, 2, iii, 4, vi, nine, 13, 19, ...} | The number of cows each year if each cow has i cow a year beginning its quaternary year. |
A000931 | Padovan sequence | {1, one, 1, ii, two, 3, 4, v, 7, 9, ...} | P(n) = P(n − 2) + P(n − three) for n ≥ 3, with P(0) = P(1) = P(2) = one. |
A000945 | Euclid–Mullin sequence | {two, 3, 7, 43, 13, 53, 5, 6221671, 38709183810571, 139, ...} | a(one) = 2; a(n + ane) is smallest prime factor of a(ane) a(ii) ⋯ a(n) + 1. |
A000959 | Lucky numbers | {1, three, vii, 9, 13, 15, 21, 25, 31, 33, ...} | A natural number in a gear up that is filtered by a sieve. |
A000961 | Prime number powers | {i, ii, 3, 4, 5, 7, 8, ix, 11, xiii, 16, 17, 19, ...} | Positive integer powers of prime numbers |
A000984 | Central binomial coefficients | {1, 2, half-dozen, 20, 70, 252, 924, ...} | , numbers in the middle of fifty-fifty rows of Pascal's triangle |
A001006 | Motzkin numbers | {1, ane, ii, 4, 9, 21, 51, 127, 323, 835, ...} | The number of ways of drawing any number of nonintersecting chords joining n (labeled) points on a circumvolve. |
A001013 | Hashemite kingdom of jordan–Pólya numbers | {1, 2, iv, 6, eight, 12, 16, 24, 32, 36, 48, 64. ...} | Numbers that are the production of factorials. |
A001045 | Jacobsthal numbers | {0, 1, 1, 3, five, 11, 21, 43, 85, 171, 341, ...} | a(northward) = a(due north − 1) + 2a(n − 2) for n ≥ 2, with a(0) = 0, a(1) = ane. |
A001065 | Sum of proper divisors s(due north) | {0, one, 1, three, i, 6, one, 7, 4, 8, ...} | s(due north) = σ(n) − due north is the sum of the proper divisors of the positive integer n . |
A001190 | Wedderburn–Etherington numbers | {0, 1, 1, one, 2, 3, six, 11, 23, 46, ...} | The number of binary rooted copse (every node has out-degree 0 or ii) with n endpoints (and 2due north − 1 nodes in all). |
A001316 | Gould'south sequence | {1, 2, 2, 4, ii, 4, 4, 8, two, 4, four, 8, 4, 8, 8, ...} | Number of odd entries in row n of Pascal's triangle. |
A001358 | Semiprimes | {4, 6, nine, 10, fourteen, 15, 21, 22, 25, 26, ...} | Products of two primes, not necessarily distinct. |
A001462 | Golomb sequence | {1, ii, 2, 3, 3, 4, 4, iv, 5, v, ...} | a(n) is the number of times northward occurs, starting with a(1) = one. |
A001608 | Perrin numbers P n | {3, 0, 2, 3, 2, 5, 5, 7, 10, 12, ...} | P(n) = P(due north−2) + P(due north−iii) for n ≥ three, with P(0) = 3, P(i) = 0, P(2) = 2. |
A001855 | Sorting number | {0, 1, three, 5, 8, 11, fourteen, 17, 21, 25, 29, 33, 37, 41, 45, 49 ...} | Used in the analysis of comparison sorts. |
A002064 | Cullen numbers C n | {i, 3, ix, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153, 106497, ...} | C north = n⋅2 n + one, with n ≥ 0. |
A002110 | Primorials p northward # | {1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, ...} | p n #, the product of the first n primes. |
A002182 | Highly blended numbers | {1, 2, iv, 6, 12, 24, 36, 48, 60, 120, ...} | A positive integer with more divisors than any smaller positive integer. |
A002201 | Superior highly composite numbers | {2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, ...} | A positive integer north for which there is an eastward > 0 such that d(n) / due north eastward ≥ d(m) / thou e for all k > ane. |
A002378 | Pronic numbers | {0, 2, six, 12, xx, thirty, 42, 56, 72, xc, ...} | a(north) = 2t(n) = n(n + one), with n ≥ 0 where t(n) are the triangular numbers. |
A002559 | Markov numbers | {1, 2, 5, 13, 29, 34, 89, 169, 194, ...} | Positive integer solutions of x 2 + y ii + z 2 = 3xyz . |
A002808 | Blended numbers | {4, 6, 8, 9, 10, 12, fourteen, 15, 16, 18, ...} | The numbers n of the course xy for x > i and y > 1. |
A002858 | Ulam number | {i, 2, 3, iv, 6, viii, eleven, 13, xvi, 18, ...} | a(1) = 1; a(ii) = 2; for n > two, a(n) is least number > a(northward − ane) which is a unique sum of two distinct earlier terms; semiperfect. |
A002863 | Prime knots | {0, 0, ane, 1, 2, 3, vii, 21, 49, 165, 552, 2176, 9988, ...} | The number of prime knots with northward crossings. |
A002997 | Carmichael numbers | {561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341, ...} | Blended numbers n such that a north − 1 ≡ 1 (mod n) if a is coprime with northward . |
A003261 | Woodall numbers | {i, 7, 23, 63, 159, 383, 895, 2047, 4607, ...} | n⋅2 due north − ane, with northward ≥ 1. |
A003601 | Arithmetic numbers | {ane, 3, 5, 6, 7, eleven, 13, xiv, xv, 17, 19, 20, 21, 22, 23, 27, ...} | An integer for which the average of its positive divisors is also an integer. |
A004490 | Colossally arable numbers | {ii, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, ...} | A number n is colossally arable if there is an ε > 0 such that for all k > 1, -
where σ denotes the sum-of-divisors function. |
A005044 | Alcuin's sequence | {0, 0, 0, 1, 0, 1, 1, 2, 1, 3, 2, 4, 3, 5, iv, 7, 5, 8, 7, x, viii, 12, ten, 14, ...} | Number of triangles with integer sides and perimeter n . |
A005100 | Deficient numbers | {1, 2, 3, 4, 5, 7, 8, 9, ten, 11, ...} | Positive integers n such that σ(n) < iidue north . |
A005101 | Arable numbers | {12, 18, xx, 24, 30, 36, forty, 42, 48, 54, ...} | Positive integers due north such that σ(n) > 2north . |
A005114 | Untouchable numbers | {2, 5, 52, 88, 96, 120, 124, 146, 162, 188, ...} | Cannot be expressed every bit the sum of all the proper divisors of any positive integer. |
A005132 | Recamán's sequence | {0, 1, 3, 6, two, 7, xiii, xx, 12, 21, xi, 22, 10, 23, 9, 24, 8, 25, 43, 62, ...} | "subtract if possible, otherwise add together": a(0) = 0; for n > 0, a(n) = a(n − i) − n if that number is positive and not already in the sequence, otherwise a(n) = a(northward − 1) + n, whether or non that number is already in the sequence. |
A005150 | Await-and-say sequence | {i, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, 13211311123113112211, ...} | A = 'frequency' followed past 'digit'-indication. |
A005153 | Practical numbers | {i, 2, 4, 6, 8, 12, xvi, xviii, 20, 24, 28, 30, 32, 36, 40...} | All smaller positive integers tin be represented every bit sums of distinct factors of the number. |
A005165 | Alternating factorial | {1, 1, v, 19, 101, 619, 4421, 35899, 326981, 3301819, 36614981, 442386619, 5784634181, 81393657019, ...} | n! − (n−1)! + (north−2)! − ... 1!. |
A005235 | Fortunate numbers | {3, v, vii, xiii, 23, 17, 19, 23, 37, 61, ...} | The smallest integer m > 1 such that p n # + grand is a prime number, where the primorial p northward # is the product of the outset n prime numbers. |
A005835 | Semiperfect numbers | {6, 12, eighteen, 20, 24, 28, xxx, 36, 40, 42, ...} | A natural number n that is equal to the sum of all or some of its proper divisors. |
A006003 | Magic constants | {15, 34, 65, 111, 175, 260, 369, 505, 671, 870, 1105, 1379, 1695, 2056, ...} | Sum of numbers in whatsoever row, cavalcade, or diagonal of a magic square of order northward ≥ three. |
A006037 | Weird numbers | {70, 836, 4030, 5830, 7192, 7912, 9272, 10430, 10570, 10792, ...} | A natural number that is abundant but not semiperfect. |
A006842 | Farey sequence numerators | {0, 1, 0, 1, 1, 0, 1, 1, ii, ane, ...} | |
A006843 | Farey sequence denominators | {1, 1, 1, 2, 1, ane, 3, ii, 3, 1, ...} | |
A006862 | Euclid numbers | {ii, 3, vii, 31, 211, 2311, 30031, 510511, 9699691, 223092871, ...} | p n # + 1, i.e. 1 + production of first due north consecutive primes. |
A006886 | Kaprekar numbers | {one, 9, 45, 55, 99, 297, 703, 999, 2223, 2728, ...} | X ii = Ab due north + B , where 0 < B < b n and Ten = A + B . |
A007304 | Sphenic numbers | {30, 42, 66, 70, 78, 102, 105, 110, 114, 130, ...} | Products of 3 distinct primes. |
A007850 | Giuga numbers | {xxx, 858, 1722, 66198, 2214408306, ...} | Blended numbers so that for each of its singled-out prime factors p i we have . |
A007947 | Radical of an integer | {1, two, iii, 2, v, 6, 7, ii, three, x, ...} | The radical of a positive integer n is the product of the distinct prime number numbers dividing n . |
A010060 | Thue–Morse sequence | {0, ane, 1, 0, 1, 0, 0, i, 1, 0, ...} | |
A014577 | Regular paperfolding sequence | {1, 1, 0, 1, 1, 0, 0, i, i, 1, ...} | At each stage an alternating sequence of 1s and 0s is inserted betwixt the terms of the previous sequence. |
A016105 | Blum integers | {21, 33, 57, 69, 77, 93, 129, 133, 141, 161, 177, ...} | Numbers of the form pq where p and q are distinct primes congruent to 3 (mod iv). |
A018226 | Magic numbers | {two, eight, 20, 28, l, 82, 126, ...} | A number of nucleons (either protons or neutrons) such that they are bundled into complete shells within the atomic nucleus. |
A019279 | Superperfect numbers | {2, 4, sixteen, 64, 4096, 65536, 262144, 1073741824, 1152921504606846976, 309485009821345068724781056, ...} | Positive integers n for which σ ii(n) = σ(σ(northward)) = 2n. |
A027641 | Bernoulli numbers B n | {ane, −ane, 1, 0, −1, 0, i, 0, −1, 0, v, 0, −691, 0, 7, 0, −3617, 0, 43867, 0, ...} | |
A034897 | Hyperperfect numbers | {half-dozen, 21, 28, 301, 325, 496, 697, ...} | 1000 -hyperperfect numbers, i.e. n for which the equality north = 1 + k (σ(n) − north − 1) holds. |
A052486 | Achilles numbers | {72, 108, 200, 288, 392, 432, 500, 648, 675, 800, ...} | Positive integers which are powerful just imperfect. |
A054377 | Primary pseudoperfect numbers | {2, 6, 42, 1806, 47058, 2214502422, 52495396602, ...} | Satisfies a certain Egyptian fraction. |
A059756 | Erdős–Woods numbers | {16, 22, 34, 36, 46, 56, 64, 66, 70, 76, 78, 86, 88, ...} | The length of an interval of consecutive integers with property that every element has a factor in common with one of the endpoints. |
A076336 | Sierpinski numbers | {78557, 271129, 271577, 322523, 327739, 482719, 575041, 603713, 903983, 934909, ...} | Odd k for which { grand⋅ii n + i : north ∈ } consists just of composite numbers. |
A076337 | Riesel numbers | {509203, 762701, 777149, 790841, 992077, ...} | Odd m for which { k⋅2 n − 1 : n ∈ } consists only of blended numbers. |
A086747 | Baum–Sweet sequence | {1, one, 0, 1, ane, 0, 0, i, 0, one, ...} | a(n) = 1 if the binary representation of n contains no block of consecutive zeros of odd length; otherwise a(n) = 0. |
A090822 | Gijswijt'southward sequence | {1, 1, 2, 1, 1, ii, 2, two, 3, 1, ...} | The northward th term counts the maximal number of repeated blocks at the end of the subsequence from 1 to n−i |
A093112 | Carol numbers | {−one, 7, 47, 223, 959, 3967, 16127, 65023, 261119, 1046527, ...} | |
A094683 | Juggler sequence | {0, i, 1, 5, 2, 11, 2, xviii, ii, 27, ...} | If n ≡ 0 (modernistic 2) and so ⌊√ n ⌋ else ⌊n 3/2⌋. |
A097942 | Highly totient numbers | {1, 2, 4, 8, 12, 24, 48, 72, 144, 240, ...} | Each number m on this list has more solutions to the equation φ(x) = k than whatever preceding chiliad . |
A122045 | Euler numbers | {1, 0, −1, 0, 5, 0, −61, 0, 1385, 0, ...} | |
A138591 | Polite numbers | {3, v, six, 7, 9, 10, 11, 12, xiii, 14, 15, 17, ...} | A positive integer that can be written equally the sum of two or more sequent positive integers. |
A194472 | Erdős–Nicolas numbers | {24, 2016, 8190, 42336, 45864, 392448, 714240, 1571328, ...} | A number north such that there exists another number g and |
A337663 | Solution to Stepping Rock Puzzle | {1, 16, 28, 38, 49, 60 ...} | The maximal value a(n) of the stepping stone puzzle |
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