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A364868 Numbers k such that 4*k+1 is the norm of a Gaussian prime.

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%I A364868 #19 Aug 21 2023 12:01:09
%S A364868 1,2,3,4,7,9,10,12,13,15,18,22,24,25,27,28,30,34,37,39,43,45,48,49,57,
%T A364868 58,60,64,67,69,70,73,78,79,84,87,88,90,93,97,99,100,102,105,108,112,
%U A364868 114,115,127,130,132,135,139,142,144,148,150,153,154,160,163,165,168,169
%N A364868 Numbers k such that 4*k+1 is the norm of a Gaussian prime.
%C A364868 Numbers k such that 4*k+1 is a prime or the square of a prime congruent to 3 modulo 4.
%C A364868 If p is a Gaussian prime of norm 4*a(n)+1 (there are two up to association if a(n) is a prime, one if a(n) is the square of a prime), then for any Gaussian integer x, we have x^a(n) == 0, 1, i, -1 or -i (mod p) where i is a primitive fourth root of unity.
%H A364868 Jianing Song, <a href="/A364868/b364868.txt">Table of n, a(n) for n = 1..10000</a>
%F A364868 a(n) = (A055025(n+1) - 1)/4.
%e A364868 2 is a term since 4*2+1 is the norm of the Gaussian prime 3.
%o A364868 (PARI) isA364868(n) = isA055025(4*n+1) \\ See A055025 for its program
%Y A364868 Cf. A055025, A364869.
%Y A364868 Contains 6*A024702 as a subsequence.
%K A364868 nonn,easy
%O A364868 1,2
%A A364868 _Jianing Song_, Aug 11 2023