A106863 Primes of the form x^2+xy+5y^2.

5, 7, 11, 17, 19, 23, 43, 47, 61, 73, 83, 101, 131, 137, 139, 149, 157, 163, 191, 197, 199, 229, 233, 239, 251, 263, 271, 277, 283, 311, 313, 347, 349, 353, 359, 367, 389, 397, 419, 443, 457, 461, 463, 467, 479, 491, 499, 503, 541, 557, 571, 577, 587, 593

Offset: 1

Author

T. D. Noe, May 09 2005

Keywords

• nonn
• easy

Comments

Discriminant=-19.

Also, primes of the form x^2-xy+5y^2 with x and y nonnegative.

Also, primes which are a square (mod 19) (or, (mod 38) - cf. A191028). - M. F. Hasler, Jan 15 2016

Also, primes p such that Legendre(-2,p) = 0 or 1. - N. J. A. Sloane, Dec 25 2017

Links

• Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 5000 terms from Vincenzo Librandi]
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Primes in A035243.

Programs

Mathematica

QuadPrimes2[1, -1, 5, 10000] (* see A106856 *)

PARI

select(p->issquare(Mod(p, 19))&&isprime(p), [1..1000]) \\ M. F. Hasler, Jan 15 2016