%I #12 Oct 26 2013 03:37:05

%S 1,1,2,2,2,1,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,

%T 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,

%U 2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2

%N Number of inequivalent Eisenstein-Jacobi primes of successive norms (indexed by A055664).

%C These are the primes in the ring of integers a+b*omega, a and b rational integers, omega = (1+sqrt(-3))/2.

%C Two primes are considered equivalent if they differ by multiplication by a unit (+-1, +-omega, +-omega^2).

%D R. K. Guy, Unsolved Problems in Number Theory, A16.

%D L. W. Reid, The Elements of the Theory of Algebraic Numbers, MacMillan, NY, 1910, see Chap. VI.

%H Jean-François Alcover, <a href="/A055666/b055666.txt">Table of n, a(n) for n = 1..1000</a>

%e 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.

%t norms = Join[{3}, Select[Range[2000], (PrimeQ[#] && Mod[#, 6] == 1) || (PrimeQ[Sqrt[#]] && Mod[Sqrt[#], 3] == 2) &]]; r[n_] := Length[Reduce[n == a^2 - a*b + b^2, {a, b}, Integers]]/6; A055666 = r /@ norms (* _Jean-François Alcover_, Oct 24 2013 *)

%Y Cf. A055664-A055668, A055025-A055029. See A004016 and A035019 for theta series of Eisenstein (or hexagonal) lattice.

%K nonn,easy,nice

%O 1,3

%A _N. J. A. Sloane_, Jun 09 2000

%E More terms from _Franklin T. Adams-Watters_, May 05 2006