A365082 Prime powers (A246655) q such that -2 is a nonzero square in the finite field F_q.

3, 9, 11, 17, 19, 25, 27, 41, 43, 49, 59, 67, 73, 81, 83, 89, 97, 107, 113, 121, 131, 137, 139, 163, 169, 179, 193, 211, 227, 233, 241, 243, 251, 257, 281, 283, 289, 307, 313, 331, 337, 347, 353, 361, 379, 401, 409, 419, 433, 443, 449, 457, 467, 491, 499, 521, 523, 529

Offset: 1

Author

Jianing Song, Oct 22 2023

Keywords

• nonn
• easy

Comments

Prime powers q that are congruent to 1 or 3 modulo 8 (see A366526).

Odd prime powers q such that (-2)^((q-1)/2) = 1 in F_q.

Prime powers q such that x^2 + 2 splits into different linear factors in F_q[x].

Contains the powers of primes congruent to 1 or 3 modulo 8 and the even powers of primes congruent to 5 or 7 modulo 8.

Examples

			49 is a term since -2 = -9 = (+-3i)^2 in F_49 = F_7(i).
		

Links

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

Crossrefs

Supersequence of A033200.

Prime powers q such that a is a nonzero square in F_q: this sequence (q=-2), A085759 (q=-1), A366526 (q=2), A365313 (q=3).

Programs

PARI

isA365082(n) = isprimepower(n) && (n%8==1 || n%8==3)