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%I #11 Apr 12 2022 09:22:58
%S 0,4,9,13,25,55,39,41,45,70,69,65,75,107,109,134,167,142,156,196,157,
%T 205,214,180,213,183,162,251,263,276,268,290,306,295,369,313,332,293,
%U 353,340,357,387,367,476,334,509,363,474,454,488,453
%N Smallest k >= 0 such that 7^k has exactly n 0's in its decimal representation.
%t a = {}; Do[k = 0; While[ Count[ IntegerDigits[7^k], 0] != n, k++ ]; a = Append[a, k], {n, 0, 50} ]; a
%t Module[{p7=DigitCount[#,10,0]&/@(7^Range[600]),nn=60},Join[{0},Flatten[ Table[ Position[p7,n,1,1],{n,nn}]]]] (* _Harvey P. Dale_, Apr 12 2022 *)
%o (PARI) A063606(n)=for(k=n, oo, #select(d->!d, digits(5^k))==n&&return(k)) \\ _M. F. Hasler_, Jun 14 2018
%Y Cf. A031146 (analog for 2^k), A063555 (analog for 3^k), A063575 (analog for 4^k), A063585 (for 5^k), A063596 (analog for 6^k).
%K base,nonn
%O 0,2
%A _Robert G. Wilson v_, Aug 10 2001