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%I #3 Mar 30 2012 17:27:06
%S 4,180,320,5480,12096,17720,82780,1175232
%N Numbers n such that 2*3^n + 1 is a primitive prime factor of 10^3^n - 1.
%C Consider the problem of finding the smallest number k such that the decimal representation of 1/k has period 3^e for a given e. The number k is usually 3^(e+2). However, if e is one of the n in this sequence, then the prime 2*3^n+1 is a smaller k. The first instance of these exceptions is 1/163, which has a period of 81.
%C Subsequence of A003306.
%C 10 must be a square residue modulo 2*3^n + 1, implying that n must be a multiple of 4.
%t Select[Range[10000], PrimeQ[1+2*3^# ] && MultiplicativeOrder[10,1+2*3^# ] == 3^# &]
%Y Cf. A003306 (primes of the form 2*3^n+1), A003060 (least k such that 1/k has period n).
%K hard,more,nonn
%O 1,1
%A _T. D. Noe_, Apr 15 2010
%E Two more terms from _Max Alekseyev_, May 03 2010
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