A208575 Product of digits of n in factorial base.

0, 1, 0, 1, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 6, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 6, 0, 0, 0, 6, 0, 12, 0, 0, 0, 9, 0, 18

Offset

0,6

Links

Antti Karttunen, Table of n, a(n) for n = 0..10080

M. R. Diamond and D. D. Reidpath, A counterexample to conjectures by Sloane and Erdős concerning the persistence of numbers, Journal of Recreational Mathematics 29:2 (1998), pp. 89-92.

Index entries for sequences related to factorial base representation

Mathematica

(* For the definition of the factorial base version of IntegerDigits, see A007623 *) Table[Times@@factBaseIntDs[n], {n, 0, 99}] (* Alonso del Arte, Feb 28 2012 *)

Prog

(PARI) a(n)=my(k=1, s=1); while(n, s*=n%k++; n\=k); s
(Python)
from functools import reduce
from operator import mul
def A(n, p=2):
    return n if n<p else A(n//p, p+1)*10 + n%p
def a(n):
    x=str(A(n - 1))
    return 0 if "0" in x else reduce(mul, [int(i) for i in x])
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jun 19 2017

Crossrefs

Cf. A007623, A007954, A031346, A208576, A208277, A227153, A227154, A227157 (positions of nonzero terms), A286590.

Sequence in context: A293959 A333146 A135767 * A355037 A365832 A070203

Adjacent sequences: A208572 A208573 A208574 * A208576 A208577 A208578

Keyword

nonn,base

Author

Charles R Greathouse IV, Feb 28 2012

Status

approved