OFFSET
0,4
COMMENTS
These are the primes in the ring of integers a+b*omega, a and b rational integers, omega = (1+sqrt(-3))/2.
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, A16.
L. W. Reid, The Elements of the Theory of Algebraic Numbers, MacMillan, NY, 1910, see Chap. VI.
FORMULA
a(n) = 6 * A055668(n). - Franklin T. Adams-Watters, May 05 2006
EXAMPLE
There are 6 Eisenstein-Jacobi primes of norm 3, omega-omega^2 times one of the 6 units [ +-1, +-omega, +-omega^2 ] but only one up to equivalence.
MATHEMATICA
a[3] = 6; a[p_ /; PrimeQ[p] && Mod[p, 6] == 1] = 12; a[n_ /; PrimeQ[p = Sqrt[n]] && Mod[p, 3] == 2] = 6; a[_] = 0; Table[a[n], {n, 0, 99}] (* Jean-François Alcover, Oct 24 2013, after Franklin T. Adams-Watters *)
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
N. J. A. Sloane, Jun 09 2000
EXTENSIONS
More terms from Franklin T. Adams-Watters, May 05 2006
STATUS
approved