A038884 Primes p such that 13 is not a square mod p.

2, 5, 7, 11, 19, 31, 37, 41, 47, 59, 67, 71, 73, 83, 89, 97, 109, 137, 149, 151, 163, 167, 193, 197, 223, 227, 229, 239, 241, 271, 281, 293, 307, 317, 331, 349, 353, 359, 379, 383, 397, 401, 409, 421, 431, 449, 457

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Inert rational primes in the field Q(sqrt(13)). - N. J. A. Sloane, Dec 26 2017

Primes that are 5, 7, 11, 15, 19, 21 mod 26. - Charles R Greathouse IV, Mar 18 2018

Links

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

Programs

Mathematica

Select[Prime@Range[120], JacobiSymbol[13, #] == -1 &] (* Vincenzo Librandi, Sep 08 2012 *)

PARI

list(lim)=my(v=List()); forprime(p=2,lim, if(kronecker(13,p)<0, listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Mar 18 2018

Formula

a(n) ~ 2n log n. - Charles R Greathouse IV, Mar 18 2018

Extensions

Offset changed from 0 to 1 by Vincenzo Librandi, Sep 08 2012