A106891 Primes of the form x^2+xy+11y^2.

11, 13, 17, 23, 31, 41, 43, 47, 53, 59, 67, 79, 83, 97, 101, 103, 107, 109, 127, 139, 167, 173, 181, 193, 197, 229, 239, 251, 269, 271, 281, 283, 293, 307, 311, 317, 337, 353, 359, 367, 379, 397, 401, 431, 439, 443, 461, 479, 487, 509, 541, 547, 557, 563

Offset: 1

Author

T. D. Noe, May 09 2005

Keywords

• nonn
• easy

Comments

Discriminant=-43.

Also, primes of the form x^2-xy+11y^2 with x and y nonnegative.

Also, primes which are a square (mod 43). - M. F. Hasler, Jan 15 2016

Also, primes p such that Legendre(-43,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 1000 terms from Vincenzo Librandi]
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Primes in A035233. Cf. A106890.

Programs

Mathematica

QuadPrimes2[1, -1, 11, 10000] (* see A106856 *)

PARI

select(p->issquare(Mod(p,43))&&isprime(p),[1..1500]) \\ M. F. Hasler, Jan 15 2016

Extensions

New definition from N. J. A. Sloane, Jun 08 2014