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 A066413 Eisenstein-Mersenne primes: primes of the form ((3 +/- sqrt(-3))/2)^p - 1. 2
 7, 271, 2269, 176419, 129159847, 1162320517, 49269609804781974450852068861184694669, 589881151426658740854227725580736348850640632297373414091790995505756623268837 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Analogs of Mersenne primes in Eisenstein integers. The norm of a + b*w is (a+b*w)*(a+b*w^2) = a^2 - a*b + b^2. REFERENCES Mike Oakes, email dated Dec 24 2001 to primenumbers(AT)yahoogroups.com LINKS K. Pershell and L. Huff, Mersenne primes in imaginary quadratic number fields, Apr 30 2002. EXAMPLE For n = 7, (1-w)^7 - 1 has norm 2269, a prime. MATHEMATICA maxPi = 40; norm[p_] := 1 + 3^p - 2*3^(p/2)*Cos[p*Pi/6]; A066413 = {}; Do[ If[ PrimeQ[ np = norm[ Prime[k] ] ], AppendTo[ A066413, np] ], {k, 1, maxPi}]; A066413 (* Jean-François Alcover, Oct 16 2012 *) CROSSREFS Cf. A066408. Sequence in context: A069449 A100465 A140031 * A332127 A222942 A289634 Adjacent sequences: A066410 A066411 A066412 * A066414 A066415 A066416 KEYWORD nonn,nice AUTHOR Mike Oakes, Dec 24 2001 EXTENSIONS Name changed by Arkadiusz Wesolowski, Apr 27 2012 STATUS approved

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Last modified March 27 12:57 EDT 2023. Contains 361570 sequences. (Running on oeis4.)