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A364869
Numbers k such that 6*k+1 is the norm of an Eisenstein prime.
2
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
1,2
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.
LINKS
FORMULA
a(n) = (A055664(n+2) - 1)/6.
EXAMPLE
4 is a term since 6*4+1 is the norm of the Eisenstein prime 5.
PROG
(PARI) isA364869(n) = isA055664(6*n+1) \\ See A055664 for its program
CROSSREFS
Contains 4*A024702 as a subsequence.
Sequence in context: A175857 A173919 A205666 * A245809 A064295 A001751
KEYWORD
nonn,easy
AUTHOR
Jianing Song, Aug 11 2023
STATUS
approved