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A055026 Number of Gaussian primes of successive norms (indexed by A055025). 4

%I

%S 4,8,4,8,8,8,8,8,4,8,8,8,8,8,8,8,8,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,

%T 8,8,8,8,4,8,8,8,8,8,8,8,8,8,8,8,8,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,

%U 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,4,8,8

%N Number of 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).

%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 m = 32; Length /@ Split[Sort[Select[Flatten[Table[{a^2 + b^2, a + b*I}, {a, -m, m}, {b, -m, m}], 1], PrimeQ[#[[2]], GaussianIntegers -> True] & ]], #1[[1]] == #2[[1]] & ][[1 ;; 87]] (* _Jean-Fran├žois Alcover_, Apr 08 2011 *)

%Y Cf. A055025-A055029, A055664-...

%K nonn,easy,nice

%O 1,1

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

%E More terms from Reiner Martin (reinermartin(AT)hotmail.com), Jul 20 2001

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Last modified February 27 21:03 EST 2020. Contains 332309 sequences. (Running on oeis4.)