A106904 Primes of the form x^2-xy+13y^2, with x and y nonnegative.

13, 19, 43, 67, 103, 127, 151, 157, 223, 229, 271, 307, 331, 349, 373, 409, 421, 433, 457, 463, 523, 577, 613, 631, 661, 727, 733, 739, 757, 769, 829, 859, 883, 919, 937, 967, 1021, 1033, 1039, 1063, 1069, 1087, 1123, 1171, 1237, 1249, 1279, 1291, 1327

Offset: 1

Author

T. D. Noe, May 09 2005

Keywords

• nonn
• easy

Comments

Discriminant=-51.

Also: Primes which are squares (mod 51). Differs from the subsequence A106903 (because x^2+xy+y^2 = (x+y)^2 - (x+y)y + y^2) from a(20) = 463 on, A106903(20) = 523. Terms which are not in A106903 are: 463, 631, 1033, 1039, 1279, 1291,... Up to 1279 these are also in A139643. Cf. also A191034. - 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, 13, 10000] (* see A106856 *)

PARI

select(p->issquare(Mod(p,51))&&isprime(p),[1..1500]) \\ See A106903 for alternative code. - M. F. Hasler, Jan 15 2016