A364869 Numbers k such that 6*k+1 is the norm of an Eisenstein prime.

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, 38, 40, 45, 46, 47, 48, 51, 52, 55, 56, 58, 61, 62, 63, 66, 68, 70, 72, 73, 76, 77, 81, 83, 87, 88, 90, 91, 95, 96, 100, 101, 102, 103, 105, 107, 110, 112, 115, 118, 121, 122, 123

Offset: 1

Author

Jianing Song, Aug 11 2023

Keywords

• nonn
• easy

Comments

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

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.

Examples

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

Links

• Jianing Song, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A055664, A364868.

Contains 4*A024702 as a subsequence.

Programs

PARI

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

Formula

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