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A066413
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Eisenstein-Mersenne primes: primes of the form ((3 +/- sqrt(-3))/2)^p - 1.
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2
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OFFSET
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1,1
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COMMENTS
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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.
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REFERENCES
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Mike Oakes, email dated Dec 24 2001 to primenumbers(AT)yahoogroups.com
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LINKS
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Table of n, a(n) for n=1..8.
K. Pershell and L. Huff, Mersenne primes in imaginary quadratic number fields, Apr 30 2002.
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EXAMPLE
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For n = 7, (1-w)^7 - 1 has norm 2269, a prime.
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A066408.
Sequence in context: A069449 A100465 A140031 * A332127 A222942 A289634
Adjacent sequences: A066410 A066411 A066412 * A066414 A066415 A066416
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KEYWORD
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nonn,nice
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AUTHOR
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Mike Oakes, Dec 24 2001
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EXTENSIONS
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Name changed by Arkadiusz Wesolowski, Apr 27 2012
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STATUS
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approved
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