A191052 Primes p that have Kronecker symbol (p|87) = 1.

2, 7, 11, 13, 17, 41, 47, 67, 89, 101, 103, 109, 113, 131, 137, 139, 151, 181, 191, 199, 223, 241, 251, 263, 269, 277, 283, 293, 311, 313, 317, 349, 359, 373, 389, 397, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 523, 547, 563, 569, 571, 599

Offset

1,1

Comments

From Jianing Song, Oct 13 2022: (Start)

Originally erroneously named "Primes that are squares mod 87".

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

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

Primes congruent to 1, 2, 4, 7, 8, 11, 13, 14, 16, 17, 22, 25, 26, 28, 32, 34, 41, 44, 47, 49, 50, 52, 56, 64, 67, 68, 77, 82 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(599) | JacobiSymbol(p, 87) eq 1]; // Vincenzo Librandi, Sep 10 2012
(PARI) isA191052(p) == isprime(p) && kronecker(p, 87) == 1 \\ Jianing Song, Oct 13 2022

Crossrefs

Cf. A191084 (rational primes that remain inert in the field Q(sqrt(-87))).

Sequence in context: A020597 A140563 A154679 * A338173 A138889 A097143

Adjacent sequences: A191049 A191050 A191051 * A191053 A191054 A191055

Keyword

nonn,easy

Author

T. D. Noe, May 25 2011

Extensions

Definition corrected by Jianing Song, Oct 13 2022

Status

approved