A274504 -id:A274504 - cp's OEIS frontend

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

Offset: 1

T. D. Noe, May 24 2011

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: (Start)
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)

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

Cf. A191018, A191020, A191061, A274504.

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

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

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

Definition corrected (following an observation by David Broadhurst) by M. F. Hasler, Jan 15 2016

A191061 Primes p that have Kronecker symbol (p|14) = -1.

Original entry on oeis.org

11, 17, 29, 31, 37, 41, 43, 47, 53, 67, 73, 89, 97, 103, 107, 109, 149, 163, 167, 179, 197, 199, 211, 223, 241, 257, 271, 277, 311, 313, 317, 331, 347, 353, 367, 373, 379, 383, 389, 409, 421, 433, 439, 443, 479, 491, 499, 503, 521, 541, 547, 557, 571, 577

Offset: 1

T. D. Noe, May 25 2011

Originally erroneously named "Primes that are not squares mod 14". - M. F. Hasler, Jan 18 2016
From Jianing Song, Nov 21 2019: (Start)
Primes congruent to {11, 17, 29, 31, 33, 37, 41, 43, 47, 51, 53, 55} mod 56.
Rational primes that are remain inert in the field Q(sqrt(-14)). (End)
Primes p such that the Legendre symbol (-14/p) = -1, i.e., -14 is not a square modulo p. - Jianing Song, Oct 23 2024

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

Cf. A191017, A274504.

[p: p in PrimesUpTo(577) | KroneckerSymbol(p, 14) eq -1]; // Vincenzo Librandi, Sep 11 2012

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

Definition corrected, following a suggestion from David Broadhurst, by M. F. Hasler, Jan 18 2016

cp's OEIS Frontend

A191017 Primes with Kronecker symbol (p|14) = 1.

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