A382313 The factorial base expansion of a(n) corresponds to the restricted growth sequence of that of n (when read from right to left).

0, 1, 5, 3, 5, 5, 15, 11, 17, 9, 23, 11, 15, 23, 23, 15, 17, 17, 15, 23, 23, 15, 23, 23, 57, 41, 59, 39, 83, 47, 63, 35, 65, 33, 95, 35, 87, 47, 71, 39, 89, 41, 87, 47, 71, 39, 119, 47, 57, 89, 83, 87, 59, 71, 87, 83, 89, 57, 71, 59, 63, 95, 95, 63, 65, 65, 87

Offset: 0

Author

Rémy Sigrist, Mar 21 2025

Keywords

• nonn
• base
• easy

Comments

We ignore nonleading zeros in factorial base expansions.

All terms belong to A120696.

Examples

			The first terms, in decimal and in factorial base, are:
  n   a(n)  fact(n)  fact(a(n))
  --  ----  -------  ----------
   0     0        0           0
   1     1        1           1
   2     5       10          21
   3     3       11          11
   4     5       20          21
   5     5       21          21
   6    15      100         211
   7    11      101         121
   8    17      110         221
   9     9      111         111
  10    23      120         321
  11    11      121         121
  12    15      200         211
  13    23      201         321
  14    23      210         321
  15    15      211         211
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..5039
• Index entries for sequences related to factorial base representation

Crossrefs

See A382269 for a similar sequence.

Cf. A120696.

Programs

PARI

a(n) = { my (v = 0, m = Map(), u = 0, d, c); for (r = 2, oo, if (n==0, return (v), d = n%r; n \= r; if (!mapisdefined(m, d, &c), mapput(m, d, c=u++);); v += c*(r-1)!;);); }

Formula

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