A106989 Primes of the form x^2-xy+23y^2, with x and y nonnegative.

23, 29, 43, 53, 79, 107, 113, 127, 179, 191, 211, 233, 263, 277, 337, 347, 373, 389, 443, 491, 547, 569, 571, 599, 641, 653, 659, 673, 701, 751, 757, 809, 823, 883, 907, 911, 919, 953, 991, 1031, 1093, 1117, 1171, 1187, 1213, 1283, 1297, 1303, 1327

Offset: 1

Author

T. D. Noe, May 09 2005

Keywords

• nonn
• easy

Comments

Discriminant=-91.

Also, primes that are squares (mod 91), or equivalently, with Legendre symbols (p|7) = (p|13) = 1. Included as subsequence in A191054 which are primes with Jacobi symbol (p|7*13) = 1, including also primes with (p|7) = (p|13) = -1. - David Broadhurst and M. F. Hasler, Jan 15 2016

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)

Programs

Mathematica

QuadPrimes2[1, -1, 23, 10000] (* see A106856 *)

PARI

is(p)=issquare(Mod(p,91))&&isprime(p) \\ M. F. Hasler, Jan 15 2016