# 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 nth term describes the length of the nth 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 ≥ 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 ≥ 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 ≥ 2, with F(0) = 0 and F(1) = 1. | A000045 |
| Sylvester's sequence | 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443, ... | $a(n+1)=\prod _{k=0}^{n}a(k)+1=a(n)^{2}-a(n)+1$ for n ≥ 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 ≥ 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: 2$^n$ 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) = 2a(n − 1) + a(n − 2) for n ≥ 2, with a(0) = 0, a(1) = 1. | A000129 |
| Factorials n! | 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, ... | $n!=\prod _{k=1}^{n}k$ for n ≥ 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$^{2n}$ + 1 for n ≥ 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 ≥ 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) ⋯ 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) + 2a(n − 2) for n ≥ 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 2n − 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 ≥ 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⋅2$^n$ + 1, with n ≥ 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 ⁠d(n)/n$^e$⁠ ≥ ⁠d(k)/k$^e$⁠ for all k > 1. | A002201 |
| Pronic numbers | 0, 2, 6, 12, 20, 30, 42, 56, 72, 90, ... | a(n) = 2t(n) = n(n + 1), with n ≥ 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$^2$ = 3xyz. | 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$^{n−1}$ ≡ 1 (mod n) if a is coprime with n. | A002997 |
| Woodall numbers | 1, 7, 23, 63, 159, 383, 895, 2047, 4607, ... | n⋅2$^n$ − 1, with n ≥ 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) < 2n. | A005100 |
| Abundant numbers | 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, ... | Positive integers n such that σ(n) > 2n. | 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, ... | $\sum _{k=0}^{n-1}(-1)^{k}(n-k)!$ | 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 ≥ 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)) = 2n. | 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 { k⋅2$^n$ + 1 : n ∈ $\mathbb {N}$ } consists only of composite numbers. | A076336 |
| Riesel numbers | 509203, 762701, 777149, 790841, 992077, ... | Odd k for which { k⋅2$^n$ − 1 : n ∈ $\mathbb {N}$ } 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 nth 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 ≡ 0 (mod 2) then ⌊√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) n ∈ $\mathbb {N}$. | 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 + ... + n for n ≥ 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 × 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)(2n + 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 × n × 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(2n$^2$ − 1), with n ≥ 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$^{p−1}$ ≡ 1 (mod p$^2$). | A001220 |
| Sophie Germain primes | 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, ... | A prime number p such that 2p + 1 is also prime. | A005384 |
| Wilson primes | 5, 13, 563 | Primes $p$ satisfying (p−1)! ≡ −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 nth Ramanujan prime is the least integer R$_n$ for which π(x) − π(x/2) ≥ n, for all x ≥ 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 ≥ 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 |