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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
Marc Chamberland, Binary BBP-Formulae for Logarithms and Generalized Gaussian-Mersenne Primes, Journal of Integer Sequences, Vol. 6 (2003), Article 03.3.7.
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: A224339 A368546 A133204 * A309588 A268614 A152658
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 19 06:25 EDT 2024. Contains 370953 sequences. (Running on oeis4.)