%I #10 Oct 30 2022 18:19:59
%S 1,2,1,2,2,2,2,2,1,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%T 2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%U 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2
%N Number of inequivalent Gaussian primes of successive norms (indexed by A055025).
%C These are the primes in the ring of integers a+bi, a and b rational integers, i = sqrt(-1).
%C Two primes are considered equivalent if they differ by multiplication by a unit (+-1, +-i).
%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. V.
%H <a href="/index/Ga#gaussians">Index entries for Gaussian integers and primes</a>
%e There are 8 Gaussian primes of norm 5, +-1+-2i and +-2+-i, but only two inequivalent ones (2+-i).
%t norms = Union[ #*Conjugate[#]& [ Select[ Flatten[ Table[a + b*I, {a, 0, 31}, {b, 0, 31}]], PrimeQ[#, GaussianIntegers -> True] &]]]; f[norm_] := (Clear[a, b]; primes = {a + b*I} /. {ToRules[ Reduce[a^2 + b^2 == norm, {a, b}, Integers]]}; primes //. {p1___, p2_, p3___, p4_, p5___} /; MatchQ[p2, (-p4 | I*p4 | -I*p4)] :> {p1, p2, p3, p5} // Length); A055027 = f /@ norms (* _Jean-François Alcover_, Nov 30 2012 *)
%Y Cf. A055025-A055029, A055664-...
%K nonn,easy,nice
%O 1,2
%A _N. J. A. Sloane_, Jun 09 2000
%E More terms from _Reiner Martin_, Jul 20 2001