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A038889 Primes p such that 17 is a square mod p. 47


%S 2,13,17,19,43,47,53,59,67,83,89,101,103,127,137,149,151,157,179,191,

%T 223,229,239,251,257,263,271,281,293,307,331,349,353,359,373,383,389,

%U 409,421,433,443,457,461,463,467,491,509,523,557,563,569,577,587,593

%N Primes p such that 17 is a square mod p.

%C 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

%C Also, primes which are a square (mod 17) (or, (mod 34), cf. A191025). - _M. F. Hasler_, Jan 15 2016

%D Z. I. Borevich and I. R. Shafarevich, Number Theory.

%D D. B. Zagier, Zetafunktionen und quadratische Koerper

%H Vincenzo Librandi, <a href="/A038889/b038889.txt">Table of n, a(n) for n = 1..1000</a>

%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)

%t Select[Prime[Range[200]],JacobiSymbol[17,#]!=-1&] (* _Harvey P. Dale_, Sep 20 2011 *)

%o (PARI) is(n)=isprime(n)&&issquare(Mod(17,n)) \\ _Charles R Greathouse IV_, Mar 21 2013

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

%Y Primes in A035258.

%K nonn

%O 1,1

%A _N. J. A. Sloane_.

%E Edited by _N. J. A. Sloane_, Jul 28 2008 at the suggestion of R. J. Mathar

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Last modified August 13 06:22 EDT 2020. Contains 336442 sequences. (Running on oeis4.)