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A207040
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Generalized Gaussian-Mersenne primes (see below).
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0
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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
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OFFSET
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1,1
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LINKS
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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
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FORMULA
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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.
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MATHEMATICA
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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]
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CROSSREFS
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Superset of A182300 (Gaussian-Mersenne primes).
Cf. A088962, A057429.
Sequence in context: A178854 A224339 A133204 * A152658 A100877 A007521
Adjacent sequences: A207037 A207038 A207039 * A207041 A207042 A207043
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KEYWORD
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nonn
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AUTHOR
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Arkadiusz Wesolowski, May 07 2012
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STATUS
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approved
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