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

Author

Rémy Sigrist, Sep 02 2020

Keywords

• nonn
• look
• base

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.

Examples

			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.
		

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

Crossrefs

See A333658 and A333659 for similar sequences.

Cf. A034968, A084558.

Programs

PARI

See Links section.

Formula

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