%I #23 Jul 20 2024 08:19:02
%S 0,8,16,76,41,1162,973,6838,25265,81782,456686,279270,1727606,6030753,
%T 23157026,106892455
%N Exponent of least power of 2 having exactly n consecutive 5's in its decimal representation.
%H Popular Computing (Calabasas, CA), <a href="/A094776/a094776.jpg">Two Tables</a>, Vol. 1, (No. 9, Dec 1973), page PC9-16.
%e a(3)=76 because 2^76 (i.e., 75557863725914323419136) is the smallest power of 2 to contain a run of 3 consecutive fives in its decimal form.
%t a = ""; Do[ a = StringJoin[a, "5"]; b = StringJoin[a, "5"]; k = 1; While[ StringPosition[ ToString[2^k], a] == {} || StringPosition[ ToString[2^k], b] != {}, k++ ]; Print[k], {n, 1, 10} ]
%K more,nonn,base
%O 0,2
%A _Shyam Sunder Gupta_, Aug 26 2007
%E 2 more terms from _Sean A. Irvine_, Jul 19 2010
%E a(13)-a(14) from _Lars Blomberg_, Jan 24 2013
%E a(0)=0 prepended by and a(15) from _Paul Geneau de Lamarlière_, Jul 19 2024