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A365313
Prime powers (A246655) q such that 3 is a nonzero square in the finite field F_q.
3
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
1,1
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.
LINKS
EXAMPLE
49 is a term since 3 = -4 = (+-2i)^2 in F_49 = F_7(i).
PROG
(PARI) isA365313(n) = isprimepower(n) && (n%12==1 || n%12==11)
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).
Sequence in context: A091998 A208296 A289696 * A023232 A075519 A019406
KEYWORD
nonn,easy
AUTHOR
Jianing Song, Oct 22 2023
STATUS
approved