A286604 a(n) = n mod sum of digits of n in factorial base.

0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 3, 0, 1, 2, 3, 0, 2, 0, 3, 0, 1, 2, 5, 0, 1, 0, 0, 1, 1, 0, 1, 2, 1, 2, 0, 0, 1, 2, 4, 0, 5, 2, 3, 4, 3, 4, 5, 0, 1, 2, 3, 0, 3, 0, 3, 0, 2, 3, 5, 0, 1, 2, 3, 4, 2, 1, 1, 2, 6, 0, 7, 0, 1, 2, 0, 1, 5, 2, 4, 0, 3, 4, 6, 4, 1, 2, 3, 4, 1, 0, 0, 1, 5, 6, 5, 0, 2, 3, 3, 4, 3, 2, 1, 2, 0, 1, 3, 0, 4, 5, 7, 0, 5, 2, 3, 4, 0, 1, 9, 0

Offset: 1

Author

Antti Karttunen, Jun 18 2017

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10080
• Index entries for sequences related to factorial base representation.

Crossrefs

Cf. A034968, A286606.

Cf. A118363 (positions of zeros), A286607 (of nonzeros).

Programs

Mathematica

a[n_] := Module[{k = n, m = 2, r, s = 0}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, s += r; m++]; Mod[n, s]]; Array[a, 100] (* Amiram Eldar, Feb 21 2024 *)

Python

def a007623(n, p=2): return n if n
Indranil Ghosh, Jun 21 2017

Scheme

(define (A286604 n) (modulo n (A034968 n)))

Formula

a(n) = n mod A034968(n).