A182300 -id:A182300 - cp's OEIS frontend

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

Marc Chamberland, Oct 28 2003

nonn

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.

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

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 *)

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.

A207040 Generalized Gaussian-Mersenne primes (see below).

Original entry on oeis.org

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

Arkadiusz Wesolowski, May 07 2012

nonn

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

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

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]

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.

cp's OEIS Frontend

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula