cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A055026 #16 Oct 30 2022 18:19:59
%S A055026 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 A055026 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 A055026 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,4,8,8
%N A055026 Number of Gaussian primes of successive norms (indexed by A055025).
%C A055026 These are the primes in the ring of integers a+bi, a and b rational integers, i = sqrt(-1).
%D A055026 R. K. Guy, Unsolved Problems in Number Theory, A16.
%D A055026 L. W. Reid, The Elements of the Theory of Algebraic Numbers, MacMillan, NY, 1910, see Chap. V.
%H A055026 <a href="/index/Ga#gaussians">Index entries for Gaussian integers and primes</a>
%e A055026 There are 8 Gaussian primes of norm 5, +-1+-2i and +-2+-i, but only two inequivalent ones (2+-i).
%t A055026 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-François Alcover_, Apr 08 2011 *)
%Y A055026 Cf. A055025-A055029, A055664-...
%K A055026 nonn,easy,nice
%O A055026 1,1
%A A055026 _N. J. A. Sloane_, Jun 09 2000
%E A055026 More terms from _Reiner Martin_, Jul 20 2001