A286606 a(n) = n mod product of nonzero digits of n in factorial base.

0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 0, 4, 5, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 0, 4, 5, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 10, 11, 0, 1, 2, 0, 4, 5, 0, 1, 2, 0, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 2, 3, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 6, 7, 8, 9, 22, 23, 0

Offset

1,20

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 A227153(n).

Mathematica

a[n_] := Module[{k = n, m = 2, r, p = 1}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, If[r > 0, p *= r]; m++]; Mod[n, p]]; Array[a, 100] (* Amiram Eldar, Feb 21 2024 *)

Prog

(Scheme) (define (A286606 n) (modulo n (A227153 n)))
(Python)
from operator import mul
from functools import reduce
def a007623(n, p=2): return n if n<p else a007623(n//p, p+1)*10 + n%p
def a(n):
    x=str(a007623(n)).replace('0', '')
    return n%reduce(mul, map(int, x))
print([a(n) for n in range(1, 201)]) # Indranil Ghosh, Jun 21 2017

Crossrefs

Cf. A227153, A286604.

Sequence in context: A336974 A084247 A300307 * A266587 A070692 A162397

Adjacent sequences: A286603 A286604 A286605 * A286607 A286608 A286609

Keyword

nonn,base

Author

Antti Karttunen, Jun 18 2017

Status

approved