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%I #2 Mar 30 2012 17:22:47
%S 0,7,7,18,19,90,91,271,1751,18807,56589,56589,56589,56589,899791,
%T 899791,2814790,7635171,7635171,39727671,99530619,233093807,233093807,
%U 233093807,233093807
%N Least k such that the last n decimal digits of 2^k are all powers of 2.
%C Does k exist for all n? This sequence is inspired by A130693, which lists all known powers of 2 whose digits are all powers of 2 (that is, 1, 2, 4, or 8).
%e 2^19=524288 is the least power of 2 ending with 5 digits that are powers of 2.
%t k=1; Join[{0}, Table[k--; pwr=PowerMod[2,k,10^n]; While[k++; pwr=Mod[2*pwr,10^n]; d=Union[IntegerDigits[pwr,10,n]]; Intersection[d,{3,5,6,7,9,0}]!={}]; k, {n,2,10}]]
%K base,nonn
%O 1,2
%A _T. D. Noe_, Apr 08 2008
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