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Smallest k >= 0 such that 9^k has exactly n 0's in its decimal representation.
6

%I #8 Jun 19 2018 05:56:33

%S 0,5,11,41,33,38,42,27,60,71,63,85,94,139,96,127,157,166,131,160,170,

%T 148,190,210,212,203,221,222,218,257,223,243,250,275,302,255,273,271,

%U 333,372,270,339,371,457,408,347,402,410,483,448,355

%N Smallest k >= 0 such that 9^k has exactly n 0's in its decimal representation.

%t a = {}; Do[k = 0; While[ Count[ IntegerDigits[9^k], 0] != n, k++ ]; a = Append[a, k], {n, 0, 50} ]; a

%o (PARI) A063626(n)=for(k=0, oo, #select(d->!d, digits(9^k))==n&&return(k)) \\ _M. F. Hasler_, Jun 15 2018

%Y Cf. A031146 (analog for 2^k), A063555 (for 3^k), A063575 (for 4^k), A063585 (for 5^k), A063596 (for 6^k), A063606 (for 7^k), A063616 (for 8^k).

%K base,nonn

%O 0,2

%A _Robert G. Wilson v_, Aug 10 2001

%E a(0) changed to 0 (as in A031146, A063555, ...) and better title from _M. F. Hasler_, Jun 15 2018