A381967 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the factorial base expansion of n*a(n) only contains distinct nonzero digits.

0, 1, 2, 4, 3, 10, 6, 7, 9, 8, 5, 12, 11, 18, 14, 16, 15, 22, 13, 19, 23, 24, 17, 20, 21, 26, 25, 40, 39, 42, 32, 54, 30, 36, 48, 62, 33, 61, 51, 28, 27, 53, 29, 67, 49, 64, 47, 46, 34, 44, 58, 38, 55, 41, 31, 52, 57, 56, 50, 59, 60, 37, 35, 66, 45, 68, 63, 43

Offset

0,3

Comments

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

This sequence is well defined: for any n > 0 and k > n, the factorial base expansion of k!, a multiple of n, contains distinct nonzero digits (in fact: a single 1 digit).

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Rémy Sigrist, Scatterplot of the first 50000 terms

Rémy Sigrist, PARI program

Index entries for sequences related to factorial base representation

Index entries for sequences that are permutations of the natural numbers

Example

The first terms, alongside the factorial base expansion of n*a(n), are:
  n   a(n)  fact(n*a(n))
  --  ----  ------------
   0     0  0
   1     1  1
   2     2  2,0
   3     4  2,0,0
   4     3  2,0,0
   5    10  2,0,1,0
   6     6  1,2,0,0
   7     7  2,0,0,1
   8     9  3,0,0,0
   9     8  3,0,0,0
  10     5  2,0,1,0
  11    12  1,0,2,0,0
  12    11  1,0,2,0,0
  13    18  1,4,3,0,0
  14    14  1,3,0,2,0
  15    16  2,0,0,0,0
  16    15  2,0,0,0,0

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A265349.

Sequence in context: A386596 A271864 A183210 * A226367 A324934 A240271

Adjacent sequences: A381964 A381965 A381966 * A381968 A381969 A381970

Keyword

nonn,base

Author

Rémy Sigrist, Mar 12 2025

Status

approved