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A227969 Powers of primes other than 2 and 5 in order by cycle length of reciprocal in decimal.

%I A227969 #12 Aug 02 2013 11:20:54
%S A227969 3,9,11,27,37,101,41,271,7,13,239,4649,73,137,81,333667,9091,21649,
%T A227969 513239,9901,53,79,265371653,909091,31,2906161,17,5882353,2071723,
%U A227969 5363222357,19,52579,1111111111111111111,3541,27961,43,1933,10838689,23,121,4093,8779,11111111111111111111111
%N A227969 Powers of primes other than 2 and 5 in order by cycle length of reciprocal in decimal.
%H A227969 Charles R Greathouse IV, <a href="/A227969/b227969.txt">Rows n = 1..100 of triangle, flattened</a>
%e A227969 3 and 9 qualify for the first 2 terms because both of them have a reciprocal cycle of 1. Then 11 has a reciprocal cycle of 2; then 27 and 37 have 3; then 101 has 4; then 41 and 271 have 5. Table begins:
%e A227969 3, 9;
%e A227969 11;
%e A227969 27, 37;
%e A227969 101;
%e A227969 41, 271;
%e A227969 7, 13;
%e A227969 239, 4649;
%e A227969 73, 137;
%e A227969 81, 333667;
%e A227969 9091;
%e A227969 21649, 513239;
%e A227969 9901;
%e A227969 53, 79, 265371653;
%o A227969 (PARI) go(n)=my(v=[],P=[],E=[],t,ok); for(k=1,n, t=setminus(factor(10^k-1)[,1]~,P); E=concat(E,vector(#t,i,1)); P=concat(P,t); E=apply(i->E[i],Vec(vecsort(P,,1))); P=vecsort(P); ok=1; while(ok, ok=0; for(i=1,#P,if(znorder(Mod(10,P[i]^(E[i]+1)))==k, E[i]++; t=concat(t,P[i]^E[i]); ok=1))); v=concat(v,t=vecsort(t)); print(k" "t)); v \\ _Charles R Greathouse IV_, Aug 01 2013
%Y A227969 Cf. A002371, A046107.
%K A227969 nonn,tabf,base
%O A227969 1,1
%A A227969 _J. Lowell_, Aug 01 2013
%E A227969 a(9)-a(43) from _Charles R Greathouse IV_, Aug 01 2013