OFFSET
1,1
COMMENTS
All terms are congruent to 2 modulo 4.
Let Phi_n(x) denote the n-th cyclotomic polynomial.
Numbers n such that Phi_{2nM(n)}(2) is prime.
Let J(n) = 2^n+1, J*(n) = the primitive part of 2^n+1, and this is Phi_{2n}(2).
Let M(n) = the Aurifeuillian M-part of 2^n+1, M(n) = 2^(n/2) + 2^((n+2)/4) + 1 for n congruent to 2 (mod 4).
Let M*(n) = GCD(M(n), J*(n)), this sequence lists all n such that M*(n) is prime.
LINKS
Eric Chen, Gord Palameta, Factorization of Phi_n(2) for n up to 1280
Samuel Wagstaff, The Cunningham project
Eric W. Weisstein's World of Mathematics, Aurifeuillean Factorization.
EXAMPLE
14 is in this sequence because the right Aurifeuillian primitive part of 2^14+1 is 29, which is prime.
26 is not in this sequence because the right Aurifeuillian primitive part of 2^26+1 is 8321, which equals 53 * 157 and is not prime.
MATHEMATICA
Select[Range[2000], Mod[n, 4] == 2 && PrimeQ[GCD[2^(n/2) + 2^((n+2)/4) + 1, Cyclotomic[2*n, 2]]]
PROG
(PARI) isok(n) = isprime(gcd(2^(n/2) + 2^((n+2)/4) + 1, polcyclo(2*n, 2))); \\ Michel Marcus, Jan 27 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric Chen, Jan 18 2015
STATUS
approved