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A364868
Numbers k such that 4*k+1 is the norm of a Gaussian prime.
2
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, 58, 60, 64, 67, 69, 70, 73, 78, 79, 84, 87, 88, 90, 93, 97, 99, 100, 102, 105, 108, 112, 114, 115, 127, 130, 132, 135, 139, 142, 144, 148, 150, 153, 154, 160, 163, 165, 168, 169
OFFSET
1,2
COMMENTS
Numbers k such that 4*k+1 is a prime or the square of a prime congruent to 3 modulo 4.
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.
LINKS
FORMULA
a(n) = (A055025(n+1) - 1)/4.
EXAMPLE
2 is a term since 4*2+1 is the norm of the Gaussian prime 3.
PROG
(PARI) isA364868(n) = isA055025(4*n+1) \\ See A055025 for its program
CROSSREFS
Contains 6*A024702 as a subsequence.
Sequence in context: A270711 A096118 A050029 * A137451 A325091 A057912
KEYWORD
nonn,easy
AUTHOR
Jianing Song, Aug 11 2023
STATUS
approved