A063585 Least k >= 0 such that 5^k has exactly n 0's in its decimal representation.

0, 8, 13, 34, 40, 48, 52, 45, 64, 99, 143, 132, 100, 122, 117, 151, 205, 207, 201, 242, 230, 244, 231, 221, 295, 264, 266, 333, 248, 344, 346, 274, 391, 345, 356, 393, 433, 365, 472, 499, 488, 455, 516, 485, 511, 458, 520, 487, 459, 456, 457

Offset: 0

Author

Robert G. Wilson v, Aug 10 2001

Keywords

• base
• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..3373
• M. F. Hasler, Zeroless powers. OEIS Wiki, March 2014

Crossrefs

Cf. A031146 (analog for 2^k), A063555 (analog for 3^k), A063575 (analog for 4^k), A063596 (analog for 6^k).

Programs

Maple

N:= 100: # to get a(0)..a(N)
A:= Array(0..N, -1):
p:= 1: A[0]:= 0:
count:= 1:
for k from 1 while count <= N do
  p:= 5*p;
  m:= numboccur(0, convert(p, base, 10));
  if m <= N and A[m] < 0 then A[m]:= k; count:= count+1;
od:
convert(A,list); # Robert Israel, Dec 20 2018

Mathematica

a = {}; Do[k = 0; While[ Count[ IntegerDigits[5^k], 0] != n, k++ ]; a = Append[a, k], {n, 0, 50} ]; a

PARI

A063585(n)=for(k=n,oo,#select(d->!d,digits(5^k))==n&&return(k)) \\ M. F. Hasler, Jun 14 2018

Extensions

a(0) changed to 0 (as in A031146, A063555, ...) and better title from M. F. Hasler, Jun 14 2018