A038889 Primes p such that 17 is a square mod p.

2, 13, 17, 19, 43, 47, 53, 59, 67, 83, 89, 101, 103, 127, 137, 149, 151, 157, 179, 191, 223, 229, 239, 251, 257, 263, 271, 281, 293, 307, 331, 349, 353, 359, 373, 383, 389, 409, 421, 433, 443, 457, 461, 463, 467, 491, 509, 523, 557, 563, 569, 577, 587, 593

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Also primes of the form 2*x^2+x*y-2*y^2 (as well as of the form 2*x^2+5*x*y+y^2). Discriminant = 17. Class = 1. This was originally a separate entry, submitted by Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), Jun 06 2008. R. J. Mathar proved that this coincides with the present sequence, Jul 22 2008

Also, primes which are a square (mod 17) (or, (mod 34), cf. A191025). - M. F. Hasler, Jan 15 2016

References

• Z. I. Borevich and I. R. Shafarevich, Number Theory.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)
• D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.

Crossrefs

Cf. A038889 (17 is a square mod p); A141111, A141112 (d=65).

Primes in A035258.

Programs

Mathematica

Select[Prime[Range[200]],JacobiSymbol[17,#]!=-1&] (* Harvey P. Dale, Sep 20 2011 *)

PARI

is(n)=isprime(n)&&issquare(Mod(17,n)) \\ Charles R Greathouse IV, Mar 21 2013

Extensions

Edited by N. J. A. Sloane, Jul 28 2008 at the suggestion of R. J. Mathar