A296929 -id:A296929 - cp's OEIS frontend

A296930 Inert rational primes in the field Q(sqrt(-17)).

5, 19, 29, 37, 41, 43, 47, 59, 61, 67, 73, 83, 97, 103, 109, 113, 127, 151, 173, 179, 181, 191, 193, 197, 223, 233, 239, 241, 251, 263, 269, 271, 277, 307, 313, 317, 331, 337, 359, 383, 397, 401, 443, 449, 463, 467, 491, 521, 523, 541, 563, 587, 599, 601, 617, 631

Offset: 1

N. J. A. Sloane, Dec 26 2017

Primes that are congruent to 5, 15, 19, 29, 35, 37, 41, 43, 45, 47, 55, 57, 59, 61, 65, or 67 mod 68. - Amiram Eldar, Nov 17 2023

Cf. A296920, A296929, A296931.

Load the Maple program HH given in A296920. Then run HH(-17, 200); This produces A296929, A296930, A296931.

Select[Prime[Range[115]], KroneckerSymbol[-17, #] == -1 &] (* Amiram Eldar, Nov 17 2023 *)

A296931 Primes p such that Legendre(-17,p) = 0 or 1.

Original entry on oeis.org

2, 3, 7, 11, 13, 17, 23, 31, 53, 71, 79, 89, 101, 107, 131, 137, 139, 149, 157, 163, 167, 199, 211, 227, 229, 257, 281, 283, 293, 311, 347, 349, 353, 367, 373, 379, 389, 409, 419, 421, 431, 433, 439, 457, 461, 479, 487, 499, 503, 509, 547, 557

Offset: 1

N. J. A. Sloane, Dec 26 2017

nonn

Primes p such that p == 1, 2, 3, 7, 9, 11, 13, 17, 21, 23, 25, 27, 31, 33, 39, 49, 53, or 63 (mod 68). - Robert Israel, Dec 26 2017

Robert Israel, Table of n, a(n) for n = 1..10000

Load the Maple program HH given in A296920. Then run HH(-17, 200); This produces A296929, A296930, A296931.
Alternative:
select(p-> isprime(p) and numtheory:-legendre(-17,p)<>-1, [2,seq(i,i=3..1000)]); # Robert Israel, Dec 26 2017

cp's OEIS Frontend

A296930 Inert rational primes in the field Q(sqrt(-17)).

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