A066413 - OEIS
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
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 *)