cp's OEIS Frontend

A226603 Let c(n) be the n-th number in the sequence of odd composite numbers that are not squares of primes, and let p = c(n)*2^k + 1 (with k > 0) and m be the smallest integer satisfying congruence 2^m == 1 (mod p). The number a(n) is the least k such that p is prime and c(n) does not divide m, or 0 if no such value exists.

%I A226603 #15 Jun 16 2013 14:25:41
%S A226603 1,1,2,6,13,2,9,13,2744,2,1,93,2,1,19,15,6,6,168,6,13,2,5,1,26,91,3,6,
%T A226603 1,5,10,18,1,293,250,11,1,41,30,5,1,8,16,4,2,497,176316,95,4,592,65,6,
%U A226603 3,113,36,1
%N A226603 Let c(n) be the n-th number in the sequence of odd composite numbers that are not squares of primes, and let p = c(n)*2^k + 1 (with k > 0) and m be the smallest integer satisfying congruence 2^m == 1 (mod p). The number a(n) is the least k such that p is prime and c(n) does not divide m, or 0 if no such value exists.
%C A226603 Since 78557 is a Sierpinski number, a(31513) = 0. Are there any values of n so that a(n) = 0 and c(n) is not a Sierpinski number?
%t A226603 lst = {}; Do[If[! PrimeQ[c] && ! PrimeQ@Sqrt[c], k = 1; While[True, p = c*2^k + 1; If[PrimeQ[p] && ! Divisible[MultiplicativeOrder[2, p], c], AppendTo[lst, k]; Break[]]; k++]], {c, 3, 185, 2}]; lst
%Y A226603 Cf. A226025.
%K A226603 hard,more,nonn
%O A226603 1,3
%A A226603 _Arkadiusz Wesolowski_, Jun 13 2013
%E A226603 a(47)-a(56) from _Arkadiusz Wesolowski_, Jun 16 2013