A191084 Primes p that have Kronecker symbol (p|87) = -1.

5, 19, 23, 31, 37, 43, 53, 59, 61, 71, 73, 79, 83, 97, 107, 127, 149, 157, 163, 167, 173, 179, 193, 197, 211, 227, 229, 233, 239, 257, 271, 281, 307, 331, 337, 347, 353, 367, 379, 383, 401, 409, 419, 421, 431, 433, 509, 521, 541, 557, 577, 587, 593, 601, 607

Offset

1,1

Comments

From Jianing Song, Oct 13 2022: (Start)

Originally erroneously named "Primes that are not squares mod 87".

Equivalently, primes p such that kronecker(-87,p) = -1.

Rational primes that remain inert in the field Q(sqrt(-87)).

Primes congruent to 5, 10, 19, 20, 23, 31, 35, 37, 38, 40, 43, 46, 53, 55, 59, 61, 62, 65, 70, 71, 73, 74, 76, 79, 80, 83, 85, 86 modulo 87. (End)

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index to sequences related to decomposition of primes in quadratic fields

Mathematica

Select[Prime[Range[200]], JacobiSymbol[#, 87]==-1&]

Prog

(Magma) [p: p in PrimesUpTo(607) | JacobiSymbol(p, 87) eq -1]; // Vincenzo Librandi, Sep 11 2012
(PARI) isA191084(p) == isprime(p) && kronecker(p, 87) == -1 \\ Jianing Song, Oct 13 2022

Crossrefs

Cf. A191052 (rational primes that decompose in the field Q(sqrt(15)))..

Sequence in context: A191054 A097934 A191609 * A146509 A062340 A167766

Adjacent sequences: A191081 A191082 A191083 * A191085 A191086 A191087

Keyword

nonn,easy

Author

T. D. Noe, May 25 2011

Extensions

Definition corrected by Jianing Song, Oct 13 2022

Status

approved