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.
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, 1, 5, 10, 18, 1, 293, 250, 11, 1, 41, 30, 5, 1, 8, 16, 4, 2, 497, 176316, 95, 4, 592, 65, 6, 3, 113, 36, 1
Offset: 1
Crossrefs
Cf. A226025.
Programs
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Mathematica
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
Extensions
a(47)-a(56) from Arkadiusz Wesolowski, Jun 16 2013
Comments