A342116 Lexicographically latest sequence of distinct nonnegative integers such that the multisets of frequencies of digits in the factorial base representations of n and of a(n) are the same.

0, 1, 5, 3, 4, 2, 21, 18, 17, 9, 23, 16, 15, 22, 20, 12, 11, 8, 7, 19, 14, 6, 13, 10, 105, 93, 90, 96, 117, 114, 63, 81, 72, 33, 113, 65, 112, 111, 108, 64, 107, 60, 104, 103, 102, 57, 119, 100, 48, 99, 98, 97, 59, 95, 94, 92, 91, 45, 89, 52, 41, 88, 87, 30

Offset: 0

Author

Rémy Sigrist, Feb 28 2021

Keywords

• nonn
• base

Comments

This sequence is a self-inverse permutation of the nonnegative integers.

Examples

			The first terms, in decimal and in factorial base, alongside the corresponding multisets of frequencies (ignoring 0's), are:
  n   a(n)  fact(n)  fact(a(n))  freq(n)
  --  ----  -------  ----------  ------------
   0     0        0           0  ()
   1     1        1           1  (1)
   2     5       10          21  (1, 1)
   3     3       11          11  (2)
   4     4       20          20  (1, 1)
   5     2       21          10  (1, 1)
   6    21      100         311  (1, 2)
   7    18      101         300  (1, 2)
   8    17      110         221  (1, 2)
   9     9      111         111  (3)
  10    23      120         321  (1, 1, 1)
  11    16      121         220  (1, 2)
  12    15      200         211  (1, 2)
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..5039
• Rémy Sigrist, Colored scatterplot of the first 8! terms (where the color is function of the multiset of frequencies of n)
• Rémy Sigrist, PARI program for A342116
• Index entries for sequences related to factorial base representation
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

See A342102 for similar sequences.

Cf. A007489, A108731.

Programs

PARI

See Links section.

Formula

a(n) < k! for any n < k!.

a(A007489(n)) = A007489(n).