A286478 Ordinal transform of A034968, factorial base digit sum.

1, 1, 2, 1, 2, 1, 3, 3, 4, 2, 3, 1, 5, 4, 5, 2, 3, 1, 6, 4, 5, 2, 3, 1, 4, 6, 7, 7, 8, 6, 8, 9, 10, 7, 8, 4, 11, 9, 10, 5, 6, 2, 11, 7, 8, 3, 4, 1, 9, 12, 13, 12, 13, 9, 14, 14, 15, 10, 11, 5, 16, 12, 13, 6, 7, 2, 14, 8, 9, 3, 4, 1, 15, 17, 18, 15, 16, 10, 19, 17, 18, 11, 12, 5, 19, 13, 14, 6, 7, 2, 15, 8, 9, 3, 4, 1, 20, 20, 21, 16, 17, 10, 22, 18, 19, 11, 12

Offset: 0

Author

Antti Karttunen, May 20 2017

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10080
• Index entries for sequences related to factorial base representation

Crossrefs

Cf. A000142, A034968, A254524 (base-10 analog).

Programs

Mathematica

f[n_] := If[n == 0, 0, Module[{s = 0, i = 2, k = n},
     While[k>0, k = Floor[n/i!]; s += (i-1) k; i++]; n-s]];
b[_] = 1;
a[n_] := a[n] = With[{t = f[n]}, b[t]++];
a /@ Range[0, 100] (* Jean-François Alcover, Dec 19 2021 *)

Formula

For all n>= 1, a(A000142(n)) = n.