A207040 Generalized Gaussian-Mersenne primes (see below).

5, 13, 29, 37, 41, 61, 109, 113, 397, 1321, 1429, 1613, 2113, 14449, 26317, 246241, 279073, 312709, 525313, 4327489, 7416361, 29247661, 47392381, 107367629, 536903681, 1326700741, 40388473189, 118750098349, 275415303169, 415878438361, 1759217765581

Offset

1,1

Links

Table of n, a(n) for n=1..31.

Marc Chamberland, Binary BBP-Formulae for Logarithms and Generalized Gaussian-Mersenne Primes, Journal of Integer Sequences, Vol. 6 (2003), Article 03.3.7.

Index entries for Gaussian integers and primes

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. See A088962 for the values of n that generate primes.

Mathematica

lst = {}; Do[s = Numerator@FullSimplify@Exp[2*Re@Log@Cyclotomic[n, (1 + I)/2]]; If[PrimeQ[s] && ! MemberQ[lst, s], AppendTo[lst, s]], {n, 2^7}]; Take[Sort[lst], 31]

Crossrefs

Supersequence of A182300 (Gaussian-Mersenne primes). Cf. A088962, A057429.

Sequence in context: A368546 A385224 A133204 * A309588 A268614 A152658

Adjacent sequences: A207037 A207038 A207039 * A207041 A207042 A207043

Keyword

nonn

Author

Arkadiusz Wesolowski, May 07 2012

Status

approved