List of integer sequences: Difference between revisions
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Latest revision as of 13:20, 26 December 2024
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 Template:Mathth term describes the length of the Template:Mathth run | Template:OEIS link |
| Euler's totient function Template:Math | 1, 1, 2, 2, 4, 2, 6, 4, 6, 4, ... | Template:Math is the number of positive integers not greater than Template:Math that are coprime with Template:Math. | Template:OEIS link |
| Lucas numbers Template:Math | 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, ... | Template:Math for Template:Math, with Template:Math and Template:Math. | Template:OEIS link |
| Prime numbers Template:Math | 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ... | The prime numbers Template:Math, with Template:Math. A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. | Template:OEIS link |
| Partition numbers Template:Math |
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, ... | The partition numbers, number of additive breakdowns of n. | Template:OEIS link |
| Fibonacci numbers Template:Math | 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... | Template:Math for Template:Math, with Template:Math and Template:Math. | Template:OEIS link |
| Sylvester's sequence | 2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443, ... | for Template:Math, with Template:Math. | Template:OEIS link |
| Tribonacci numbers | 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, ... | Template:Math for Template:Math, with Template:Math. | Template:OEIS link |
| Powers of 2 | 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ... | Powers of 2: 2n for n ≥ 0 | Template:OEIS link |
| Polyominoes | 1, 1, 1, 2, 5, 12, 35, 108, 369, ... | The number of free polyominoes with Template:Math cells. | Template:OEIS link |
| Catalan numbers Template:Math | 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, ... | Template:OEIS link | |
| Bell numbers Template:Math | 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, ... | Template:Math is the number of partitions of a set with Template:Math elements. | Template:OEIS link |
| Euler zigzag numbers Template:Math | 1, 1, 1, 2, 5, 16, 61, 272, 1385, 7936, ... | Template:Math is the number of linear extensions of the "zig-zag" poset. | Template:OEIS link |
| 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 Template:Math cuts. | Template:OEIS link |
| Pell numbers Template:Math | 0, 1, 2, 5, 12, 29, 70, 169, 408, 985, ... | Template:Math for Template:Math, with Template:Math. | Template:OEIS link |
| Factorials Template:Math | 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, ... | for Template:Math, with Template:Math (empty product). | Template:OEIS link |
| Derangements | 1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, 14684570, 176214841, ... | Number of permutations of n elements with no fixed points. | Template:OEIS link |
| Divisor function Template:Math | 1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, ... | Template:Math is the sum of divisors of a positive integer Template:Math. | Template:OEIS link |
| Fermat numbers Template:Math | 3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, 340282366920938463463374607431768211457, ... | Template:Math for Template:Math. | Template:OEIS link |
| Polytrees | 1, 1, 3, 8, 27, 91, 350, 1376, 5743, 24635, 108968, ... | Number of oriented trees with n nodes. | Template:OEIS link |
| Perfect numbers | 6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128, ... | Template:Math is equal to the sum Template:Math of the proper divisors of Template:Math. | Template:OEIS link |
| Ramanujan tau function | 1, −24, 252, −1472, 4830, −6048, −16744, 84480, −113643, ... | Values of the Ramanujan tau function, Template:Math at n = 1, 2, 3, ... | Template:OEIS link |
| Landau's function | 1, 1, 2, 3, 4, 6, 6, 12, 15, 20, ... | The largest order of permutation of Template:Math elements. | Template:OEIS link |
| 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. | Template:OEIS link |
| Padovan sequence | 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, ... | Template:Math for Template:Math, with Template:Math. | Template:OEIS link |
| Euclid–Mullin sequence | 2, 3, 7, 43, 13, 53, 5, 6221671, 38709183810571, 139, ... | Template:Math is smallest prime factor of Template:Math. | Template:OEIS link |
| Lucky numbers | 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, ... | A natural number in a set that is filtered by a sieve. | Template:OEIS link |
| Prime powers | 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, ... | Positive integer powers of prime numbers | Template:OEIS link |
| Central binomial coefficients | 1, 2, 6, 20, 70, 252, 924, ... | , numbers in the center of even rows of Pascal's triangle | Template:OEIS link |
| Motzkin numbers | 1, 1, 2, 4, 9, 21, 51, 127, 323, 835, ... | The number of ways of drawing any number of nonintersecting chords joining Template:Math (labeled) points on a circle. | Template:OEIS link |
| Jordan–Pólya numbers | 1, 2, 4, 6, 8, 12, 16, 24, 32, 36, 48, 64, ... | Numbers that are the product of factorials. | Template:OEIS link |
| Jacobsthal numbers | 0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, ... | Template:Math for Template:Math, with Template:Math. | Template:OEIS link |
| Sum of proper divisors Template:Math | 0, 1, 1, 3, 1, 6, 1, 7, 4, 8, ... | Template:Math is the sum of the proper divisors of the positive integer Template:Math. | Template:OEIS link |
| 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 Template:Math endpoints (and Template:Math nodes in all). | Template:OEIS link |
| 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. | Template:OEIS link |
| Semiprimes | 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ... | Products of two primes, not necessarily distinct. | Template:OEIS link |
| Golomb sequence | 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, ... | Template:Math is the number of times Template:Math occurs, starting with Template:Math. | Template:OEIS link |
| Perrin numbers Template:Math | 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, ... | Template:Math for Template:Math, with Template:Math. | Template:OEIS link |
| 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. | Template:OEIS link |
| Cullen numbers Template:Math | 1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153, 106497, ... | Template:Math, with Template:Math. | Template:OEIS link |
| Primorials Template:Math | 1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, ... | Template:Math, the product of the first Template:Math primes. | Template:OEIS link |
| Highly composite numbers | 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, ... | A positive integer with more divisors than any smaller positive integer. | Template:OEIS link |
| Superior highly composite numbers | 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, ... | A positive integer Template:Math for which there is an Template:Math such that Template:Math for all Template:Math. | Template:OEIS link |
| Pronic numbers | 0, 2, 6, 12, 20, 30, 42, 56, 72, 90, ... | Template:Math, with Template:Math where Template:Math are the triangular numbers. | Template:OEIS link |
| Markov numbers | 1, 2, 5, 13, 29, 34, 89, 169, 194, ... | Positive integer solutions of Template:Math. | Template:OEIS link |
| Composite numbers | 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, ... | The numbers Template:Math of the form Template:Math for Template:Math and Template:Math. | Template:OEIS link |
| Ulam number | 1, 2, 3, 4, 6, 8, 11, 13, 16, 18, ... | Template:Math for Template:Math is least number Template:Math which is a unique sum of two distinct earlier terms; semiperfect. | Template:OEIS link |
| Prime knots | 0, 0, 1, 1, 2, 3, 7, 21, 49, 165, 552, 2176, 9988, ... | The number of prime knots with n crossings. | Template:OEIS link |
| Carmichael numbers | 561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341, ... | Composite numbers Template:Math such that Template:Math if Template:Math is coprime with Template:Math. | Template:OEIS link |
| Woodall numbers | 1, 7, 23, 63, 159, 383, 895, 2047, 4607, ... | Template:Math, with Template:Math. | Template:OEIS link |
| 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. | Template:OEIS link |
| Colossally abundant numbers | 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, ... | A number n is colossally abundant if there is an Template:Math such that for all Template:Math,
where Template:Mvar denotes the sum-of-divisors function. |
Template:OEIS link |
| 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 Template:Math. | Template:OEIS link |
| Deficient numbers | 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, ... | Positive integers Template:Math such that Template:Math. | Template:OEIS link |
| Abundant numbers | 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, ... | Positive integers Template:Math such that Template:Math. | Template:OEIS link |
| 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. | Template:OEIS link |
| 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. | Template:OEIS link |
| Look-and-say sequence | 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, 13211311123113112211, ... | A = 'frequency' followed by 'digit'-indication. | Template:OEIS link |
| 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. | Template:OEIS link |
| Alternating factorial | 1, 1, 5, 19, 101, 619, 4421, 35899, 326981, 3301819, 36614981, 442386619, 5784634181, 81393657019, ... | Template:OEIS link | |
| Fortunate numbers | 3, 5, 7, 13, 23, 17, 19, 23, 37, 61, ... | The smallest integer Template:Math such that Template:Math is a prime number, where the primorial Template:Math is the product of the first Template:Math prime numbers. | Template:OEIS link |
| Semiperfect numbers | 6, 12, 18, 20, 24, 28, 30, 36, 40, 42, ... | A natural number Template:Math that is equal to the sum of all or some of its proper divisors. | Template:OEIS link |
| 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 Template:Math. | Template:OEIS link |
| Weird numbers | 70, 836, 4030, 5830, 7192, 7912, 9272, 10430, 10570, 10792, ... | A natural number that is abundant but not semiperfect. | Template:OEIS link |
| Farey sequence numerators | 0, 1, 0, 1, 1, 0, 1, 1, 2, 1, ... | Template:OEIS link | |
| Farey sequence denominators | 1, 1, 1, 2, 1, 1, 3, 2, 3, 1, ... | Template:OEIS link | |
| Euclid numbers | 2, 3, 7, 31, 211, 2311, 30031, 510511, 9699691, 223092871, ... | Template:Math, i.e. Template:Math product of first Template:Math consecutive primes. | Template:OEIS link |
| Kaprekar numbers | 1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728, ... | Template:Math, where Template:Math and Template:Math. | Template:OEIS link |
| Sphenic numbers | 30, 42, 66, 70, 78, 102, 105, 110, 114, 130, ... | Products of 3 distinct primes. | Template:OEIS link |
| Giuga numbers | 30, 858, 1722, 66198, 2214408306, ... | Composite numbers so that for each of its distinct prime factors pi we have . | Template:OEIS link |
| Radical of an integer | 1, 2, 3, 2, 5, 6, 7, 2, 3, 10, ... | The radical of a positive integer Template:Math is the product of the distinct prime numbers dividing Template:Math. | Template:OEIS link |
| Thue–Morse sequence | 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, ... | Template:OEIS link | |
| 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. | Template:OEIS link |
| Blum integers | 21, 33, 57, 69, 77, 93, 129, 133, 141, 161, 177, ... | Numbers of the form Template:Math where Template:Mvar and Template:Mvar are distinct primes congruent to Template:Math. | Template:OEIS link |
| 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. | Template:OEIS link |
| Superperfect numbers | 2, 4, 16, 64, 4096, 65536, 262144, 1073741824, 1152921504606846976, 309485009821345068724781056, ... | Positive integers Template:Math for which Template:Math | Template:OEIS link |
| Bernoulli numbers Template:Math | 1, −1, 1, 0, −1, 0, 1, 0, −1, 0, 5, 0, −691, 0, 7, 0, −3617, 0, 43867, 0, ... | Template:OEIS link | |
| Hyperperfect numbers | 6, 21, 28, 301, 325, 496, 697, ... | Template:Math-hyperperfect numbers, i.e. Template:Math for which the equality Template:Math holds. | Template:OEIS link |
| Achilles numbers | 72, 108, 200, 288, 392, 432, 500, 648, 675, 800, ... | Positive integers which are powerful but imperfect. | Template:OEIS link |
| Primary pseudoperfect numbers | 2, 6, 42, 1806, 47058, 2214502422, 52495396602, ... | Satisfies a certain Egyptian fraction. | Template:OEIS link |
| 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. | Template:OEIS link |
| Sierpinski numbers | 78557, 271129, 271577, 322523, 327739, 482719, 575041, 603713, 903983, 934909, ... | Odd Template:Math for which Template:Math consists only of composite numbers. | Template:OEIS link |
| Riesel numbers | 509203, 762701, 777149, 790841, 992077, ... | Odd Template:Math for which Template:Math consists only of composite numbers. | Template:OEIS link |
| Baum–Sweet sequence | 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, ... | Template:Math if the binary representation of Template:Math contains no block of consecutive zeros of odd length; otherwise Template:Math. | Template:OEIS link |
| Gijswijt's sequence | 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, ... | The Template:Mathth term counts the maximal number of repeated blocks at the end of the subsequence from Template:Math to Template:Math | Template:OEIS link |
| Carol numbers | −1, 7, 47, 223, 959, 3967, 16127, 65023, 261119, 1046527, ... | Template:OEIS link | |
| Juggler sequence | 0, 1, 1, 5, 2, 11, 2, 18, 2, 27, ... | If Template:Math then Template:Math else Template:Math. | Template:OEIS link |
| Highly totient numbers | 1, 2, 4, 8, 12, 24, 48, 72, 144, 240, ... | Each number Template:Mvar on this list has more solutions to the equation Template:Math than any preceding Template:Math. | Template:OEIS link |
| Euler numbers | 1, 0, −1, 0, 5, 0, −61, 0, 1385, 0, ... | Template:OEIS link | |
| 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. | Template:OEIS link |
| Erdős–Nicolas numbers | 24, 2016, 8190, 42336, 45864, 392448, 714240, 1571328, ... | A number Template:Mvar such that there exists another number Template:Mvar and | Template:OEIS link |
| Solution to Stepping Stone Puzzle | 1, 16, 28, 38, 49, 60, ... | The maximal value Template:Math of the stepping stone puzzle | Template:OEIS link |
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) Template:Math. | Template:OEIS link |
| Triangular numbers Template:Math | 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, ... | Template:Math for Template:Math, with Template:Math (empty sum). | Template:OEIS link |
| Square numbers Template:Math | 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, ... | Template:Math | Template:OEIS link |
| Tetrahedral numbers Template:Math | 0, 1, 4, 10, 20, 35, 56, 84, 120, 165, ... | Template:Math is the sum of the first Template:Math triangular numbers, with Template:Math (empty sum). | Template:OEIS link |
| Square pyramidal numbers | 0, 1, 5, 14, 30, 55, 91, 140, 204, 285, ... | Template:Math: The number of stacked spheres in a pyramid with a square base. | Template:OEIS link |
| Cube numbers Template:Math | 0, 1, 8, 27, 64, 125, 216, 343, 512, 729, ... | Template:Math | Template:OEIS link |
| Fifth powers | 0, 1, 32, 243, 1024, 3125, 7776, 16807, 32768, 59049, 100000, ... | Template:Math | Template:OEIS link |
| Star numbers | 1, 13, 37, 73, 121, 181, 253, 337, 433, 541, 661, 793, 937, ... | Sn = 6n(n − 1) + 1. | Template:OEIS link |
| Stella octangula numbers | 0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990, 2651, 3444, 4381, ... | Stella octangula numbers: Template:Math, with Template:Math. | Template:OEIS link |
Types of primes
| Name | First elements | Short description | OEIS |
|---|---|---|---|
| Mersenne prime exponents | 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, ... | Primes Template:Math such that Template:Math is prime. | Template:OEIS link |
| Mersenne primes | 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, ... | Template:Math is prime, where Template:Math is a prime. | Template:OEIS link |
| Wagstaff primes | 3, 11, 43, 683, 2731, 43691, ... | A prime number p of the form where q is an odd prime. | Template:OEIS link |
| Wieferich primes | 1093, 3511 | Primes satisfying Template:Math. | Template:OEIS link |
| Sophie Germain primes | 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, ... | A prime number Template:Math such that Template:Math is also prime. | Template:OEIS link |
| Wilson primes | 5, 13, 563 | Primes satisfying Template:Math. | Template:OEIS link |
| 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 Template:Math. | Template:OEIS link |
| 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). | Template:OEIS link |
| Wolstenholme primes | 16843, 2124679 | Primes satisfying . | Template:OEIS link |
| Ramanujan primes | 2, 11, 17, 29, 41, 47, 59, 67, ... | The Template:Mathth Ramanujan prime is the least integer Template:Math for which Template:Math, for all Template:Math. | Template:OEIS link |
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. | Template:OEIS link |
| 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. | Template:OEIS link |
| Permutable primes | 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, ... | The numbers for which every permutation of digits is a prime. | Template:OEIS link |
| 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). | Template:OEIS link |
| Factorions | 1, 2, 145, 40585, ... | A natural number that equals the sum of the factorials of its decimal digits. | Template:OEIS link |
| Circular primes | 2, 3, 5, 7, 11, 13, 17, 37, 79, 113, ... | The numbers which remain prime under cyclic shifts of digits. | Template:OEIS link |
| Home prime | 1, 2, 3, 211, 5, 23, 7, 3331113965338635107, 311, 773, ... | For Template:Math is the prime that is finally reached when you start with Template:Math, concatenate its prime factors (A037276) and repeat until a prime is reached; Template:Math if no prime is ever reached. | Template:OEIS link |
| Undulating numbers | 101, 121, 131, 141, 151, 161, 171, 181, 191, 202, ... | A number that has the digit form Template:Math. | Template:OEIS link |
| 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. | Template:OEIS link |
| 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). | Template:OEIS link |
| Pandigital numbers | 1023456789, 1023456798, 1023456879, 1023456897, 1023456978, 1023456987, 1023457689, 1023457698, 1023457869, 1023457896, ... | Numbers containing the digits Template:Math such that each digit appears exactly once. | Template:OEIS link |