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

1,5

Links

Antti Karttunen, Table of n, a(n) for n = 1..10080

Index entries for sequences related to factorial base representation.

Formula

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

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 *)

Prog

(Scheme) (define (A286604 n) (modulo n (A034968 n)))
(Python)
def a007623(n, p=2): return n if n<p else a007623(n//p, p+1)*10 + n%p
def a(n):
    return n % sum(int(k) for k in str(a007623(n)))
print([a(n) for n in range(1, 201)]) # Indranil Ghosh, Jun 21 2017

Crossrefs

Cf. A034968, A286606.

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

Sequence in context: A078979 A063974 A144628 * A366784 A217540 A226861

Adjacent sequences: A286601 A286602 A286603 * A286605 A286606 A286607

Keyword

nonn,base

Author

Antti Karttunen, Jun 18 2017

Status

approved