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

0,3

Comments

We ignore nonleading zeros in factorial base expansions.

All terms belong to A382262.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..5039

Index entries for sequences related to factorial base representation

Example

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

Prog

(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; ); }

Crossrefs

Cf. A382262.

Sequence in context: A133773 A327555 A346915 * A077934 A077950 A077973

Adjacent sequences: A382266 A382267 A382268 * A382270 A382271 A382272

Keyword

nonn,base

Author

Rémy Sigrist, Mar 20 2025

Status

approved