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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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

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

FORMULA

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

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

EXAMPLE

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)

PROG

(PARI) See Links section.

CROSSREFS

See A342102 for similar sequences.

Cf. A007489, A108731.

Sequence in context: A243359 A222229 A168360 * A342117 A107488 A114236

Adjacent sequences:  A342113 A342114 A342115 * A342117 A342118 A342119

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Feb 28 2021

STATUS

approved

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Last modified October 26 00:52 EDT 2021. Contains 348256 sequences. (Running on oeis4.)