The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A250198 Numbers n such that the right Aurifeuillian primitive part of 2^n+1 is prime. 1
 2, 6, 10, 14, 18, 22, 30, 34, 38, 42, 54, 58, 66, 70, 90, 102, 110, 114, 126, 138, 170, 178, 242, 294, 314, 326, 350, 378, 462, 566, 646, 726, 758, 1150, 1242, 1302, 1482, 1558, 1638, 1710, 1770, 1970, 1994 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A250197, A153443, A019320, A072226, A161508, A085601, A229768, A061443. Sequence in context: A290490 A182991 A278568 * A260084 A194282 A000952 Adjacent sequences:  A250195 A250196 A250197 * A250199 A250200 A250201 KEYWORD nonn AUTHOR Eric Chen, Jan 18 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 21 19:07 EST 2021. Contains 340352 sequences. (Running on oeis4.)