A365313 Prime powers (A246655) q such that 3 is a nonzero square in the finite field F_q.

11, 13, 23, 25, 37, 47, 49, 59, 61, 71, 73, 83, 97, 107, 109, 121, 131, 157, 167, 169, 179, 181, 191, 193, 227, 229, 239, 241, 251, 263, 277, 289, 311, 313, 337, 347, 349, 359, 361, 373, 383, 397, 409, 419, 421, 431, 433, 443, 457, 467, 479, 491, 503, 529, 541, 563

Offset: 1

Author

Jianing Song, Oct 22 2023

Keywords

• nonn
• easy

Comments

Prime powers q that are congruent to 1 or 11 modulo 12 (see A366526).

Odd prime powers q such that 3^((q-1)/2) = 1 in F_q.

Prime powers q such that x^2 - 3 splits into different linear factors in F_q[x].

Contains the powers of primes congruent to 1 or 11 modulo 12 and the even powers of primes congruent to 5 or 7 modulo 12.

Examples

			49 is a term since 3 = -4 = (+-2i)^2 in F_49 = F_7(i).
		

Links

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

Crossrefs

Supersequence of A097933.

Prime powers q such that a is a nonzero square in F_q: A365082 (q=-2), A085759 (q=-1), A366526 (q=2), this sequence (q=3).

Programs

PARI

isA365313(n) = isprimepower(n) && (n%12==1 || n%12==11)