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

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

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

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

Cf. A055025, A364869.

Contains 6*A024702 as a subsequence.

Sequence in context: A270711 A096118 A050029 * A137451 A325091 A057912

Adjacent sequences: A364865 A364866 A364867 * A364869 A364870 A364871

Keyword

nonn,easy

Author

Jianing Song, Aug 11 2023

Status

approved