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

%I A063585 #14 Dec 20 2018 22:33:40
%S A063585 0,8,13,34,40,48,52,45,64,99,143,132,100,122,117,151,205,207,201,242,
%T A063585 230,244,231,221,295,264,266,333,248,344,346,274,391,345,356,393,433,
%U A063585 365,472,499,488,455,516,485,511,458,520,487,459,456,457
%N A063585 Least k >= 0 such that 5^k has exactly n 0's in its decimal representation.
%H A063585 Robert Israel, <a href="/A063585/b063585.txt">Table of n, a(n) for n = 0..3373</a>
%H A063585 M. F. Hasler, <a href="https://oeis.org/wiki/Zeroless_powers">Zeroless powers</a>. OEIS Wiki, March 2014
%p A063585 N:= 100: # to get a(0)..a(N)
%p A063585 A:= Array(0..N, -1):
%p A063585 p:= 1: A[0]:= 0:
%p A063585 count:= 1:
%p A063585 for k from 1 while count <= N do
%p A063585   p:= 5*p;
%p A063585   m:= numboccur(0, convert(p, base, 10));
%p A063585   if m <= N and A[m] < 0 then A[m]:= k; count:= count+1;
%p A063585 od:
%p A063585 convert(A,list); # _Robert Israel_, Dec 20 2018
%t A063585 a = {}; Do[k = 0; While[ Count[ IntegerDigits[5^k], 0] != n, k++ ]; a = Append[a, k], {n, 0, 50} ]; a
%o A063585 (PARI) A063585(n)=for(k=n,oo,#select(d->!d,digits(5^k))==n&&return(k)) \\ _M. F. Hasler_, Jun 14 2018
%Y A063585 Cf. A031146 (analog for 2^k), A063555 (analog for 3^k), A063575 (analog for 4^k), A063596 (analog for 6^k).
%K A063585 base,nonn
%O A063585 0,2
%A A063585 _Robert G. Wilson v_, Aug 10 2001
%E A063585 a(0) changed to 0 (as in A031146, A063555, ...) and better title from _M. F. Hasler_, Jun 14 2018