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%I #8 Jun 26 2018 19:14:41
%S 1,4,12,10,20,32,30,68,49,73,82,93,125,103,109,131,146,119,161,113,
%T 172,163,191,197,199,240,232,243,210,217,288,317,292,289,321,333,319,
%U 327,276,374,358,397,354,357,373,452,428,489,391,516,470
%N Smallest k such that 7^k has exactly n 2's in its decimal representation.
%t a = {}; Do[k = 1; While[ Count[ IntegerDigits[7^k], 2] != n, k++ ]; a = Append[a, k], {n, 0, 50} ]; a
%t With[{pwrs=7^Range[600]},Log[7,#]&/@Table[SelectFirst[pwrs, DigitCount[ #,10,2] == n&], {n,0,50}]] (* The program uses the SelectFirst function from Mathematica version 10 *) (* _Harvey P. Dale_, Aug 25 2015 *)
%K base,nonn
%O 0,2
%A _Robert G. Wilson v_, Aug 10 2001
%E Name corrected by _Jon E. Schoenfield_, Jun 26 2018