%I
%S 7,13,23,31,43,47,59,67,71,101,103,139,167,179,191,263,277,283,293,
%T 311,383,431,439,443,503,547,557,599,607,613,653,683,787,809,827,853,
%U 859,863,887,947,983,997,1013,1019,1039,1163,1213,1237,1321,1367,1399,1423
%N Primes p for which the period length of 1/p is a semiprime.
%C The prime index of A122183. Semiprime analog of A072859 = primes p for which the period length of 1/p is prime. Based upon A002371 = period of decimal expansion of 1/(nth prime).
%H Ray Chandler, <a href="/A129727/b129727.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 7 because A000040(4) Period of decimal expansion of 1/7 = 6 = 2*3, a semiprime.
%e a(2) = 13 because A000040(6) = 6 = 2*3.
%e a(3) = 23 because A000040(9) = 22 = 2*11.
%e a(4) = 31 because A000040(11) = 15 = 3*5.
%e a(5) = 43 because A000040(14) = 21 = 3*7.
%e a(6) = 47 because A000040(15) = 46 = 2*23.
%e a(7) = 59 because A000040(17) = 58 = 2*29.
%t fQ[p_] := Plus @@ Last /@ FactorInteger@Length@RealDigits[1/p][[1, 1]] == 2;; lst = {}; Do[ p = Prime@n; If[ fQ@p, AppendTo[lst, p]], {n, 230}] (* _Robert G. Wilson v_ *)
%Y Cf. A000040, A001358, A002371, A072859, A128948.
%K base,easy,nonn
%O 1,1
%A _Jonathan Vos Post_, May 12 2007
