A366526 -id:A366526 - cp's OEIS frontend

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

Jianing Song, Oct 22 2023

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.

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

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

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).

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

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

Original entry on oeis.org

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

Jianing Song, Oct 22 2023

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.

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

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

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).

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

cp's OEIS Frontend

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

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