A191059 Primes p that have Kronecker symbol (p|6) = -1.

13, 17, 19, 23, 37, 41, 43, 47, 61, 67, 71, 89, 109, 113, 137, 139, 157, 163, 167, 181, 191, 211, 229, 233, 239, 257, 263, 277, 281, 283, 307, 311, 331, 349, 353, 359, 373, 379, 383, 397, 401, 421, 431, 449, 479, 499, 503, 521, 523, 541, 547, 569, 571, 593

Offset: 1

Author

T. D. Noe, May 25 2011

Keywords

• nonn
• easy

Comments

Inert rational primes in the field Q(sqrt(-6)). - N. J. A. Sloane, Dec 26 2017

Appears to be the primes p such that (p mod 6)*(Fibonacci(p) mod 6) = 5. - Gary Detlefs, May 26 2014

Originally erroneously named "Primes that are not squares mod 6". - M. F. Hasler, Jan 18 2016

From Jianing Song, Oct 23 2024: (Start)

Primes p such that the Legendre symbol (-6/p) = -1, i.e., -6 is not a square modulo p.

Primes congruent to {13, 17, 19, 23} module 24. (End)

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index to sequences related to decomposition of primes in quadratic fields

Crossrefs

Cf. A157437.

Programs

Magma

[p: p in PrimesUpTo(593) | KroneckerSymbol(p, 6) eq -1]; // Vincenzo Librandi, Sep 11 2012

Mathematica

Select[Prime[Range[200]], JacobiSymbol[#,6]==-1&]

PARI

is(n)=isprime(n) && kronecker(n,6)<0 \\ Charles R Greathouse IV, Feb 23 2017

Extensions

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