A191055 Primes p that have Kronecker symbol (p|93) = 1.

7, 11, 17, 19, 23, 29, 53, 67, 83, 89, 97, 103, 109, 137, 157, 163, 167, 179, 193, 197, 211, 239, 251, 263, 269, 283, 307, 347, 349, 353, 373, 379, 383, 389, 397, 401, 421, 439, 449, 461, 491, 509, 541, 547, 557, 569, 577, 587, 607, 641, 647, 661, 677, 691

Offset

1,1

Comments

From Jianing Song, Oct 13 2022: (Start)

Originally erroneously named "Primes that are squares mod 93".

Equivalently, primes p such that kronecker(93,p) = 1.

Rational primes that decompose in the field Q(sqrt(93)).

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[#, 93]==1&]

Prog

(Magma) [p: p in PrimesUpTo(691) | JacobiSymbol(p, 93) eq 1]; // Vincenzo Librandi, Sep 10 2012
(PARI) isA191055(p) == isprime(p) && kronecker(p, 93) == 1 \\ Jianing Song, Oct 13 2022

Crossrefs

A038981, the sequence of primes that do not remain inert in the field Q(sqrt(93)), is essentially the same.

Cf. A038982 (rational primes that remain inert in the field Q(sqrt(93)))..

Sequence in context: A346991 A038880 A019365 * A078497 A274505 A256567

Adjacent sequences: A191052 A191053 A191054 * A191056 A191057 A191058

Keyword

nonn,easy

Author

T. D. Noe, May 25 2011

Extensions

Definition corrected by Jianing Song, Oct 13 2022

Status

approved