%I #18 Aug 21 2023 12:01:04

%S 1,2,3,4,5,6,7,10,11,12,13,16,17,18,20,21,23,25,26,27,30,32,33,35,37,

%T 38,40,45,46,47,48,51,52,55,56,58,61,62,63,66,68,70,72,73,76,77,81,83,

%U 87,88,90,91,95,96,100,101,102,103,105,107,110,112,115,118,121,122,123

%N Numbers k such that 6*k+1 is the norm of an Eisenstein prime.

%C Numbers k such that 6*k+1 is a prime or the square of a prime congruent to 5 modulo 6.

%C If p is an Eisenstein prime of norm 6*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 Eisenstein integer x, we have x^a(n) == 0, 1, w, w^2, -1, -w or -w^2 (mod p), where w = (1+sqrt(-3))/2 is a primitive sixth root of unity.

%H Jianing Song, <a href="/A364869/b364869.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = (A055664(n+2) - 1)/6.

%e 4 is a term since 6*4+1 is the norm of the Eisenstein prime 5.

%o (PARI) isA364869(n) = isA055664(6*n+1) \\ See A055664 for its program

%Y Cf. A055664, A364868.

%Y Contains 4*A024702 as a subsequence.

%K nonn,easy

%O 1,2

%A _Jianing Song_, Aug 11 2023