List of integer sequences

This is a list of notable integer sequences with links to their entries in the On-Line Encyclopedia of Integer Sequences.

General

Name	First elements	Short description	OEIS
Kolakoski sequence	{1, 2, 2, 1, 1, 2, 1, 2, 2, 1, ...}	The $n$ th term describes the length of the $n$ th run	A000002
Euler's totient function $φ (n)$	{1, 1, 2, 2, 4, 2, 6, 4, 6, 4, ...}	$φ (n)$ is the number of positive integers not greater than $n$ that are coprime with $n$ .	A000010
Lucas numbers $L (n)$	{2, 1, 3, 4, 7, 11, 18, 29, 47, 76, ...}	$L (n) = L (n - 1) + L (n - 2)$ for $n \geq 2$ , with $L (0) = 2$ and $L (1) = 1$ .	A000032
Prime numbers $p n$	{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...}	The prime numbers $p n$ , with $n \geq 1$ . A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers.	A000040
Partition numbers $P n$	{1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, ...}	The partition numbers, number of additive breakdowns of n.	A000041
Fibonacci numbers $F (n)$	{0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...}	$F (n) = F (n - 1) + F (n - 2)$ for $n \geq 2$ , with $F (0) = 0$ and $F (1) = 1$ .	A000045
Sylvester's sequence	{2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443, ...}	$a (n + 1) = a (n) \cdot a (n - 1) \cdot \dots \cdot a (0) + 1 = a (n) 2 - a (n) + 1$ for $n \geq 1$ , with $a (0) = 2$ .	A000058
Tribonacci numbers	{0, 1, 1, 2, 4, 7, 13, 24, 44, 81, ...}	$T (n) = T (n - 1) + T (n - 2) + T (n - 3)$ for $n \geq 3$ , with $T (0) = 0 and T (1) = T (2) = 1$ .	A000073
Powers of 2	{1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...}	Powers of 2: 2ⁿ for n ≥ 0	A000079
Polyominoes	{1, 1, 1, 2, 5, 12, 35, 108, 369, ...}	The number of free polyominoes with $n$ cells.	A000105
Catalan numbers $C n$	{1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, ...}	$C_{n}={\frac {1}{n+1}}{2n \choose n}={\frac {(2n)!}{(n+1)!\,n!}}=\prod \limits _{k=2}^{n}{\frac {n+k}{k}},\quad n\geq 0.$	A000108
Bell numbers $B n$	{1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, ...}	$B n$ is the number of partitions of a set with $n$ elements.	A000110
Euler zigzag numbers $E n$	{1, 1, 1, 2, 5, 16, 61, 272, 1385, 7936, ...}	$E n$ is the number of linear extensions of the "zig-zag" poset.	A000111
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.	A000124
Pell numbers $P n$	{0, 1, 2, 5, 12, 29, 70, 169, 408, 985, ...}	$a (n) = 2 a (n - 1) + a (n - 2)$ for $n \geq 2$ , with $a (0) = 0, a (1) = 1$ .	A000129
Factorials $n!$	{1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, ...}	$n! = 1 \cdot 2 \cdot 3 \cdot 4 \cdot \dots \cdot n$ for $n \geq 1$ , with $0! = 1$ (empty product).	A000142
Derangements	{1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, 14684570, 176214841, ...}	Number of permutations of n elements with no fixed points.	A000166
Divisor function $σ (n)$	{1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, ...}	$σ (n) := σ 1 (n)$ is the sum of divisors of a positive integer $n$ .	A000203
Fermat numbers $F n$	{3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, 340282366920938463463374607431768211457, ...}	$F n = 2 2 n + 1$ for $n \geq 0$ .	A000215
Polytrees	{1, 1, 3, 8, 27, 91, 350, 1376, 5743, 24635, 108968, ...}	Number of oriented trees with n nodes.	A000238
Perfect numbers	{6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128, ...}	$n$ is equal to the sum $s (n) = σ (n) - n$ of the proper divisors of $n$ .	A000396
Ramanujan tau function	{1,−24,252,−1472,4830,−6048,−16744,84480,−113643...}	Values of the Ramanujan tau function, $τ (n)$ at n = 1, 2, 3, ...	A000594
Landau's function	{1, 1, 2, 3, 4, 6, 6, 12, 15, 20, ...}	The largest order of permutation of $n$ elements.	A000793
Narayana's cows	{1, 1, 1, 2, 3, 4, 6, 9, 13, 19, ...}	The number of cows each year if each cow has one cow a year beginning its fourth year.	A000930
Padovan sequence	{1, 1, 1, 2, 2, 3, 4, 5, 7, 9, ...}	$P (n) = P (n - 2) + P (n - 3)$ for $n \geq 3$ , with $P (0) = P (1) = P (2) = 1$ .	A000931
Euclid–Mullin sequence	{2, 3, 7, 43, 13, 53, 5, 6221671, 38709183810571, 139, ...}	$a (1) = 2; a (n + 1)$ is smallest prime factor of $a (1) a (2) \dots a (n) + 1$ .	A000945
Lucky numbers	{1, 3, 7, 9, 13, 15, 21, 25, 31, 33, ...}	A natural number in a set that is filtered by a sieve.	A000959
Prime powers	{2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, ...}	Positive integer powers of prime numbers	A000961
Central binomial coefficients	{1, 2, 6, 20, 70, 252, 924, ...}	${2n \choose n}={\frac {(2n)!}{(n!)^{2}}}{\text{ for all }}n\geq 0$ , numbers in the center of even rows of Pascal's triangle	A000984
Motzkin numbers	{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.	A001006
Jordan–Pólya numbers	{1, 2, 4, 6, 8, 12, 16, 24, 32, 36, 48, 64. ...}	Numbers that are the product of factorials.	A001013
Jacobsthal numbers	{0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, ...}	$a (n) = a (n - 1) + 2 a (n - 2)$ for $n \geq 2$ , with $a (0) = 0, a (1) = 1$ .	A001045
Sum of proper divisors $s (n)$	{0, 1, 1, 3, 1, 6, 1, 7, 4, 8, ...}	$s (n) = σ (n) - n$ is the sum of the proper divisors of the positive integer $n$ .	A001065
Wedderburn–Etherington numbers	{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).	A001190
Gould's sequence	{1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, ...}	Number of odd entries in row n of Pascal's triangle.	A001316
Semiprimes	{4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ...}	Products of two primes, not necessarily distinct.	A001358
Golomb sequence	{1, 2, 2, 3, 3, 4, 4, 4, 5, 5, ...}	$a (n)$ is the number of times $n$ occurs, starting with $a (1) = 1$ .	A001462
Perrin numbers $P n$	{3, 0, 2, 3, 2, 5, 5, 7, 10, 12, ...}	$P (n) = P (n -2) + P (n -3)$ for $n \geq 3$ , with $P (0) = 3, P (1) = 0, P (2) = 2$ .	A001608
Sorting number	{0, 1, 3, 5, 8, 11, 14, 17, 21, 25, 29, 33, 37, 41, 45, 49 ...}	Used in the analysis of comparison sorts.	A001855
Cullen numbers $C n$	{1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153, 106497, ...}	$C n = n \cdot 2 n + 1$ , with $n \geq 0$ .	A002064
Primorials $p n #$	{1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, ...}	$p n #$ , the product of the first $n$ primes.	A002110
Highly composite numbers	{1, 2, 4, 6, 12, 24, 36, 48, 60, 120, ...}	A positive integer with more divisors than any smaller positive integer.	A002182
Superior highly composite numbers	{2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, ...}	A positive integer $n$ for which there is an $e > 0$ such that $.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num,.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0 0.1em}.mw-parser-output .sfrac .den{border-top:1px solid}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}d(n)/ne ≥ d(k)/ke$ for all $k > 1$ .	A002201
Pronic numbers	{0, 2, 6, 12, 20, 30, 42, 56, 72, 90, ...}	$a (n) = 2 t (n) = n (n + 1)$ , with $n \geq 0$ where $t (n)$ are the triangular numbers.	A002378
Markov numbers	{1, 2, 5, 13, 29, 34, 89, 169, 194, ...}	Positive integer solutions of $x 2 + y 2 + z 2 = 3 xyz$ .	A002559
Composite numbers	{4, 6, 8, 9, 10, 12, 14, 15, 16, 18, ...}	The numbers $n$ of the form $xy$ for $x > 1$ and $y > 1$ .	A002808
Ulam number	{1, 2, 3, 4, 6, 8, 11, 13, 16, 18, ...}	$a (1) = 1; a (2) = 2;$ for $n > 2, a (n)$ is least number $> a (n - 1)$ which is a unique sum of two distinct earlier terms; semiperfect.	A002858
Prime knots	{0, 0, 1, 1, 2, 3, 7, 21, 49, 165, 552, 2176, 9988, ...}	The number of prime knots with n crossings.	A002863
Carmichael numbers	{561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341, ...}	Composite numbers $n$ such that $a n - 1 \equiv 1 (mod n)$ if $a$ is coprime with $n$ .	A002997
Woodall numbers	{1, 7, 23, 63, 159, 383, 895, 2047, 4607, ...}	$n \cdot 2 n - 1$ , with $n \geq 1$ .	A003261
Arithmetic numbers	{1, 3, 5, 6, 7, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 27, ...}	An integer for which the average of its positive divisors is also an integer.	A003601
Colossally abundant numbers	{2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, ...}	A number n is colossally abundant if there is an ε > 0 such that for all k > 1, ${\frac {\sigma (n)}{n^{1+\varepsilon }}}\geq {\frac {\sigma (k)}{k^{1+\varepsilon }}},$ where $σ$ denotes the sum-of-divisors function.	A004490
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 $n$ .	A005044
Deficient numbers	{1, 2, 3, 4, 5, 7, 8, 9, 10, 11, ...}	Positive integers $n$ such that $σ (n) < 2 n$ .	A005100
Abundant numbers	{12, 18, 20, 24, 30, 36, 40, 42, 48, 54, ...}	Positive integers $n$ such that $σ (n) > 2 n$ .	A005101
Untouchable numbers	{2, 5, 52, 88, 96, 120, 124, 146, 162, 188, ...}	Cannot be expressed as the sum of all the proper divisors of any positive integer.	A005114
Recamán's sequence	{0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, ...}	"subtract if possible, otherwise add": a(0) = 0; for n > 0, a(n) = a(n − 1) − n if that number is positive and not already in the sequence, otherwise a(n) = a(n − 1) + n, whether or not that number is already in the sequence.	A005132
Look-and-say sequence	{1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, 13211311123113112211, ...}	A = 'frequency' followed by 'digit'-indication.	A005150
Practical numbers	{1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40...}	All smaller positive integers can be represented as sums of distinct factors of the number.	A005153
Alternating factorial	{1, 1, 5, 19, 101, 619, 4421, 35899, 326981, 3301819, 36614981, 442386619, 5784634181, 81393657019, ...}	n! − (n−1)! + (n−2)! − ... 1!.	A005165
Fortunate numbers	{3, 5, 7, 13, 23, 17, 19, 23, 37, 61, ...}	The smallest integer $m > 1$ such that $p n # + m$ is a prime number, where the primorial $p n #$ is the product of the first $n$ prime numbers.	A005235
Semiperfect numbers	{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.	A005835
Magic constants	{15, 34, 65, 111, 175, 260, 369, 505, 671, 870, 1105, 1379, 1695, 2056, ...}	Sum of numbers in any row, column, or diagonal of a magic square of order $n \geq 3$ .	A006003
Weird numbers	{70, 836, 4030, 5830, 7192, 7912, 9272, 10430, 10570, 10792, ...}	A natural number that is abundant but not semiperfect.	A006037
Farey sequence numerators	{0, 1, 0, 1, 1, 0, 1, 1, 2, 1, ...}		A006842
Farey sequence denominators	{1, 1, 1, 2, 1, 1, 3, 2, 3, 1, ...}		A006843
Euclid numbers	{2, 3, 7, 31, 211, 2311, 30031, 510511, 9699691, 223092871, ...}	$p n # + 1$ , i.e. $1 +$ product of first $n$ consecutive primes.	A006862
Kaprekar numbers	{1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728, ...}	$X 2 = Ab n + B$ , where $0 < B < b n$ and $X = A + B$ .	A006886
Sphenic numbers	{30, 42, 66, 70, 78, 102, 105, 110, 114, 130, ...}	Products of 3 distinct primes.	A007304
Giuga numbers	{30, 858, 1722, 66198, 2214408306, ...}	Composite numbers so that for each of its distinct prime factors p_i we have $p_{i}^{2}\,\|\,(n-p_{i})$ .	A007850
Radical of an integer	{1, 2, 3, 2, 5, 6, 7, 2, 3, 10, ...}	The radical of a positive integer $n$ is the product of the distinct prime numbers dividing $n$ .	A007947
Thue–Morse sequence	{0, 1, 1, 0, 1, 0, 0, 1, 1, 0, ...}		A010060
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.	A014577
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 $3 (mod 4)$ .	A016105
Magic numbers	{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.	A018226
Superperfect numbers	{2, 4, 16, 64, 4096, 65536, 262144, 1073741824, 1152921504606846976, 309485009821345068724781056, ...}	Positive integers $n$ for which $σ 2 (n) = σ (σ (n)) = 2 n .$	A019279
Bernoulli numbers $B n$	{1, −1, 1, 0, −1, 0, 1, 0, −1, 0, 5, 0, −691, 0, 7, 0, −3617, 0, 43867, 0, ...}		A027641
Hyperperfect numbers	{6, 21, 28, 301, 325, 496, 697, ...}	$k$ -hyperperfect numbers, i.e. $n$ for which the equality $n = 1 + k (σ (n) - n - 1)$ holds.	A034897
Achilles numbers	{72, 108, 200, 288, 392, 432, 500, 648, 675, 800, ...}	Positive integers which are powerful but imperfect.	A052486
Primary pseudoperfect numbers	{2, 6, 42, 1806, 47058, 2214502422, 52495396602, ...}	Satisfies a certain Egyptian fraction.	A054377
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.	A059756
Sierpinski numbers	{78557, 271129, 271577, 322523, 327739, 482719, 575041, 603713, 903983, 934909, ...}	Odd $k$ for which $\mathbb {N}$ consists only of composite numbers.	A076336
Riesel numbers	{509203, 762701, 777149, 790841, 992077, ...}	Odd $k$ for which $\mathbb {N}$ consists only of composite numbers.	A076337
Baum–Sweet sequence	{1, 1, 0, 1, 1, 0, 0, 1, 0, 1, ...}	$a (n) = 1$ if the binary representation of $n$ contains no block of consecutive zeros of odd length; otherwise $a (n) = 0$ .	A086747
Gijswijt's sequence	{1, 1, 2, 1, 1, 2, 2, 2, 3, 1, ...}	The $n$ th term counts the maximal number of repeated blocks at the end of the subsequence from $1$ to $n -1$	A090822
Carol numbers	{−1, 7, 47, 223, 959, 3967, 16127, 65023, 261119, 1046527, ...}	$a(n)=(2^{n}-1)^{2}-2.$	A093112
Juggler sequence	{0, 1, 1, 5, 2, 11, 2, 18, 2, 27, ...}	If $n \equiv 0 (mod 2)$ then $⌊ \sqrt n ⌋$ else $⌊ n 3/2 ⌋$ .	A094683
Highly totient numbers	{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 $k$ .	A097942
Euler numbers	{1, 0, −1, 0, 5, 0, −61, 0, 1385, 0, ...}	${\frac {1}{\cosh t}}={\frac {2}{e^{t}+e^{-t}}}=\sum _{n=0}^{\infty }{\frac {E_{n}}{n!}}\cdot t^{n}.$	A122045
Polite numbers	{3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, ...}	A positive integer that can be written as the sum of two or more consecutive positive integers.	A138591
Erdős–Nicolas numbers	{24, 2016, 8190, 42336, 45864, 392448, 714240, 1571328, ...}	A number $n$ such that there exists another number $m$ and $\sum _{d\mid n,\ d\leq m}\!d=n.$	A194472
Solution to Stepping Stone Puzzle	{1, 16, 28, 38, 49, 60 ...}	The maximal value $a (n)$ of the stepping stone puzzle	A337663

Figurate numbers

Name	First elements	Short description	OEIS
Natural numbers	{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...}	The natural numbers (positive integers) $\mathbb {N}$ .	A000027
Triangular numbers $t (n)$	{0, 1, 3, 6, 10, 15, 21, 28, 36, 45, ...}	$t (n) = C (n + 1, 2) = n (n + 1) / 2 = 1 + 2 + \dots + n$ for $n \geq 1$ , with $t (0) = 0$ (empty sum).	A000217
Square numbers $n 2$	{0, 1, 4, 9, 16, 25, 36, 49, 64, 81, ...}	$n 2 = n \times n$	A000290
Tetrahedral numbers $T (n)$	{0, 1, 4, 10, 20, 35, 56, 84, 120, 165, ...}	$T (n)$ is the sum of the first $n$ triangular numbers, with $T (0) = 0$ (empty sum).	A000292
Square pyramidal numbers	{0, 1, 5, 14, 30, 55, 91, 140, 204, 285, ...}	$n (n + 1)(2 n + 1) / 6$ : The number of stacked spheres in a pyramid with a square base.	A000330
Cube numbers $n 3$	{0, 1, 8, 27, 64, 125, 216, 343, 512, 729, ...}	$n 3 = n \times n \times n$	A000578
Fifth powers	{0, 1, 32, 243, 1024, 3125, 7776, 16807, 32768, 59049, 100000, ...}	$n 5$	A000584
Star numbers	{1, 13, 37, 73, 121, 181, 253, 337, 433, 541, 661, 793, 937, ...}	S_n = 6n(n − 1) + 1.	A003154
Stella octangula numbers	{0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990, 2651, 3444, 4381, ...}	Stella octangula numbers: $n (2 n 2 - 1)$ , with $n \geq 0$ .	A007588

Types of primes

Name	First elements	Short description	OEIS
Mersenne prime exponents	{2, 3, 5, 7, 13, 17, 19, 31, 61, 89, ...}	Primes $p$ such that $2 p - 1$ is prime.	A000043
Mersenne primes	{3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, ...}	$2 p - 1$ is prime, where $p$ is a prime.	A000668
Wagstaff primes	{3, 11, 43, 683, 2731, 43691, ...}	A prime number p of the form $p={{2^{q}+1} \over 3}$ where q is an odd prime.	A000979
Wieferich primes	{1093, 3511}	Primes $p$ satisfying $2 p -1 \equiv 1 (mod p 2)$ .	A001220
Sophie Germain primes	{2, 3, 5, 11, 23, 29, 41, 53, 83, 89, ...}	A prime number $p$ such that $2 p + 1$ is also prime.	A005384
Wilson primes	{5, 13, 563}	Primes $p$ satisfying $(p -1)! \equiv -1 (mod p 2)$ .	A007540
Happy numbers	{1, 7, 10, 13, 19, 23, 28, 31, 32, 44, ...}	The numbers whose trajectory under iteration of sum of squares of digits map includes $1$ .	A007770
Factorial primes	{2, 3, 5, 7, 23, 719, 5039, 39916801, ...}	A prime number that is one less or one more than a factorial (all factorials > 1 are even).	A088054
Wolstenholme primes	{16843, 2124679}	Primes $p$ satisfying ${2p-1 \choose p-1}\equiv 1{\pmod {p^{4}}}$ .	A088164
Ramanujan primes	{2, 11, 17, 29, 41, 47, 59, 67, ...}	The $n$ ^th Ramanujan prime is the least integer $R n$ for which $π (x) - π (x /2) \geq n$ , for all $x \geq R n$ .	A104272

Base-dependent

Name	First elements	Short description	OEIS
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.	A005224
Palindromic numbers	{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121...}	A number that remains the same when its digits are reversed.	A002113
Permutable primes	{2, 3, 5, 7, 11, 13, 17, 31, 37, 71, ...}	The numbers for which every permutation of digits is a prime.	A003459
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).	A005349
Factorions	{1, 2, 145, 40585, ...}	A natural number that equals the sum of the factorials of its decimal digits.	A014080
Circular primes	{2, 3, 5, 7, 11, 13, 17, 37, 79, 113, ...}	The numbers which remain prime under cyclic shifts of digits.	A016114
Home prime	{1, 2, 3, 211, 5, 23, 7, 3331113965338635107, 311, 773, ...}	For $n \geq 2, a (n)$ is 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.	A037274
Undulating numbers	{101, 121, 131, 141, 151, 161, 171, 181, 191, 202, ...}	A number that has the digit form $ababab$ .	A046075
Equidigital numbers	{1, 2, 3, 5, 7, 10, 11, 13, 14, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 35, 37, 41, 43, 47, 49, 53, 59, 61, 64, ...}	A number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1.	A046758
Extravagant numbers	{4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30, 33, 34, 36, 38, ...}	A number that has fewer digits than the number of digits in its prime factorization (including exponents).	A046760
Pandigital numbers	{1023456789, 1023456798, 1023456879, 1023456897, 1023456978, 1023456987, 1023457689, 1023457698, 1023457869, 1023457896, ...}	Numbers containing the digits $0-9$ such that each digit appears exactly once.	A050278

References

OEIS core sequences

External links

Index to OEIS

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