A365082 - OEIS

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

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OFFSET

1,1

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.

LINKS

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

EXAMPLE

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

PROG

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

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).

Sequence in context: A190238 A047471 A354938 * A201544 A225771 A215816

Adjacent sequences: A365079 A365080 A365081 * A365083 A365084 A365085

KEYWORD

nonn,easy

AUTHOR

Jianing Song, Oct 22 2023

STATUS

approved