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

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..3373

M. F. Hasler, Zeroless powers. OEIS Wiki, March 2014

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

Prog

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

Crossrefs

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

Sequence in context: A321483 A096371 A354595 * A258768 A048851 A039298

Adjacent sequences: A063582 A063583 A063584 * A063586 A063587 A063588

Keyword

base,nonn

Author

Robert G. Wilson v, Aug 10 2001

Extensions

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

Status

approved