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Smallest k such that 5^k has exactly n 3's in its decimal representation.
1

%I #14 Jan 28 2025 13:40:29

%S 1,5,17,25,32,48,35,90,84,81,128,101,140,120,159,145,179,154,181,104,

%T 224,234,226,246,261,228,315,323,316,320,259,303,359,325,377,317,369,

%U 415,457,439,476,473,493,470,513,548,508,472,529,533,601

%N Smallest k such that 5^k has exactly n 3's in its decimal representation.

%H Harvey P. Dale, <a href="/A063588/b063588.txt">Table of n, a(n) for n = 0..1000</a>

%t a = {}; Do[k = 1; While[ Count[ IntegerDigits[5^k], 3] != n, k++ ]; a = Append[a, k], {n, 0, 50} ]; a

%t With[{tbl=Table[{n,DigitCount[5^n,10,3]},{n,700}]},Table[SelectFirst[tbl,#[[2]]==k&],{k,0,50}]][[;;,1]] (* _Harvey P. Dale_, Jan 28 2025 *)

%K base,nonn

%O 0,2

%A _Robert G. Wilson v_, Aug 10 2001

%E Name corrected by _Jon E. Schoenfield_, Jun 26 2018