A088962 Values of n that generate Generalized Gaussian-Mersenne primes (see below).

2, 3, 4, 5, 7, 9, 10, 11, 12, 14, 15, 18, 19, 21, 22, 26, 27, 29, 30, 33, 34, 35, 42, 45, 47, 49, 51, 54, 55, 58, 63, 65, 66, 69, 70, 73, 79, 85, 86, 87, 105, 106, 110, 111, 113, 114, 126, 129, 138, 147, 151, 157, 163, 167, 178, 186, 189, 217, 231, 239, 241, 242, 283

Offset: 1

Author

Marc Chamberland, Oct 28 2003

Keywords

• nonn

Links

• M. Chamberland, Binary BBP-Formulae for Logarithms and Generalized Gaussian-Mersenne Primes, Journal of Integer Sequences, v.6 (2003), article 03.3.7, 1-10.

Crossrefs

Cf. A057429, A182300 (Gaussian-Mersenne primes).

Programs

Mathematica

t = {}; Do[s = FullSimplify[Exp[2 Re[Log [Cyclotomic[n, (1 + I)/2]]]]]; If[PrimeQ[Numerator[s]], AppendTo[t, n]], {n, 100}]; t (* T. D. Noe, May 02 2012 *)

Formula

The numerator of the rational expression exp(2*Re(log(Phi_n((1+i)/2)))) is prime, where Phi_n is the n-th cyclotomic polynomial.