A382269 The factorial base expansion of a(n) is, when read from right to left, the ordinal transform of that of n.

0, 1, 3, 5, 3, 3, 11, 15, 15, 23, 9, 15, 11, 9, 9, 11, 15, 15, 11, 9, 9, 11, 9, 9, 47, 63, 63, 83, 39, 57, 59, 87, 87, 119, 57, 87, 35, 57, 57, 83, 39, 63, 35, 57, 57, 83, 33, 57, 47, 39, 39, 35, 63, 57, 35, 39, 39, 47, 57, 63, 59, 57, 57, 59, 87, 87, 35, 33

Offset: 0

Author

Rémy Sigrist, Mar 20 2025

Keywords

• nonn
• base

Comments

We ignore nonleading zeros in factorial base expansions.

All terms belong to A382262.

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     3  1,0      1,1
   3     5  1,1      2,1
   4     3  2,0      1,1
   5     3  2,1      1,1
   6    11  1,0,0    1,2,1
   7    15  1,0,1    2,1,1
   8    15  1,1,0    2,1,1
   9    23  1,1,1    3,2,1
  10     9  1,2,0    1,1,1
  11    15  1,2,1    2,1,1
  12    11  2,0,0    1,2,1
  13     9  2,0,1    1,1,1
  14     9  2,1,0    1,1,1
  15    11  2,1,1    1,2,1
  16    15  2,2,0    2,1,1
		

Links

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

Crossrefs

Cf. A382262.

Programs

PARI

a(n) = { my (v = 0, d, f = [0]); for (r = 2, oo, if (n==0, return (v); ); if (#f < r, f = concat(f, vector(#f)); ); v += f[1+(n % r)]++*(r-1)!; n \= r; ); }