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A207040 Generalized Gaussian-Mersenne primes (see below). 0
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 (list; graph; refs; listen; history; text; internal format)
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: A178854 A224339 A133204 * A309588 A268614 A152658

Adjacent sequences:  A207037 A207038 A207039 * A207041 A207042 A207043

KEYWORD

nonn

AUTHOR

Arkadiusz Wesolowski, May 07 2012

STATUS

approved

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Last modified January 26 20:42 EST 2020. Contains 331288 sequences. (Running on oeis4.)