A337598 a(n) is the greatest number m not yet in the sequence such that the factorial base expansions of n and of m have the same digits (up to order but with multiplicity).

0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 14, 15, 12, 13, 10, 11, 16, 17, 18, 20, 19, 21, 22, 23, 24, 30, 26, 32, 54, 56, 25, 31, 27, 33, 55, 57, 50, 51, 38, 39, 62, 63, 78, 80, 79, 81, 86, 87, 48, 49, 36, 37, 60, 61, 28, 34, 29, 35, 58, 59, 52, 53, 40, 41, 64, 65, 84, 85

Offset

0,3

Comments

Leading 0's are ignored.

This sequence is a permutation of the nonnegative integers, which preserves the number of digits (A084558) and the sum of digits (A034968) in factorial base.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..5039

Rémy Sigrist, Scatterplot of the first 9! terms

Rémy Sigrist, PARI program for A337598

Index entries for sequences related to factorial base representation

Index entries for sequences that are permutations of the natural numbers

Formula

a(n!) = n! for any n >= 0.

Example

For n = 42:
- the factorial base expansion of 42 is "1300",
- there are four numbers m with the same multiset of digits:
     m   fact(m)
     --  -------
     42  "1300"
     73  "3001"
     74  "3010"
     78  "3100"
- so a(42) = 78,
     a(73) = 74,
     a(74) = 73,
     a(78) = 42.

Prog

(PARI) See Links section.

Crossrefs

See A333658 and A333659 for similar sequences.

Cf. A034968, A084558.

Sequence in context: A078840 A358124 A333658 * A333221 A334438 A185974

Adjacent sequences: A337595 A337596 A337597 * A337599 A337600 A337601

Keyword

nonn,look,base

Author

Rémy Sigrist, Sep 02 2020

Status

approved