A191017 - OEIS

A191017

Primes with Kronecker symbol (p|14) = 1.

3, 5, 13, 19, 23, 59, 61, 71, 79, 83, 101, 113, 127, 131, 137, 139, 151, 157, 173, 181, 191, 193, 227, 229, 233, 239, 251, 263, 269, 281, 283, 293, 307, 337, 349, 359, 397, 401, 419, 431, 449, 457, 461, 463, 467, 487, 509, 523, 563, 569, 587, 599, 617, 619

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OFFSET

1,1

COMMENTS

Originally incorrectly named "Primes that are squares mod 14", which is sequence A045373. - M. F. Hasler, Jan 15 2016

Conjecture: primes congruent to {1, 3, 5, 9, 13, 15, 19, 23, 25, 27, 39, 45} mod 56. - Vincenzo Librandi, Jun 22 2016

From Jianing Song, Nov 21 2019:

Rational primes that decompose in the field Q(sqrt(-14)).

These are primes p such that either one of (a) p == 1, 2, 4 (mod 7), p == 1, 7 (mod 8) or (b) p == 3, 5, 6 (mod 7), p == 3, 5 (mod 8) holds. So the conjecture above is correct. (End)

LINKS

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

MATHEMATICA

Select[Prime[Range[200]], JacobiSymbol[#, 14]==1&]

PROG

(Magma) [p: p in PrimesUpTo(619) | KroneckerSymbol(p, 14) eq 1]; // Vincenzo Librandi, Sep 11 2012

(PARI) is(p)=kronecker(p, 14)==1&&isprime(p) \\ Michel Marcus, Jun 23 2016 after A191032

CROSSREFS

Cf. A191018, A191020, A191061, A274504.

Sequence in context: A108702 A136053 A157468 * A228228 A227031 A157974

Adjacent sequences: A191014 A191015 A191016 * A191018 A191019 A191020

KEYWORD