A106861 Primes of the form x^2+xy+4y^2, with x and y nonnegative.

19, 31, 79, 109, 151, 181, 199, 211, 229, 271, 331, 349, 409, 421, 439, 499, 571, 601, 619, 631, 661, 691, 709, 769, 811, 829, 859, 919, 991, 1021, 1039, 1051, 1069, 1129, 1171, 1201, 1249, 1291, 1321, 1381, 1399, 1429, 1459, 1471, 1489, 1531, 1579

Offset: 1

Author

T. D. Noe, May 09 2005

Keywords

• nonn
• easy

Comments

Discriminant=-15.

Subset of A033212. - Robert Israel, Jul 25 2014

Links

• Vincenzo Librandi and Rick L. Shepherd, Table of n, a(n) for n = 1..10000 (first 2000 terms from Vincenzo Librandi)
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Cf. A033212.

Programs

Maple

N:= 1000; # to get all terms <= N
Primes:= select(isprime,[seq(2*n+1,n=1..floor((N-1)/2))]):
filter:= proc(p) local S;
  S:= remove(hastype,[isolve(x^2+x*y+4*y^2=p)],negint);
  nops(S) > 0
end proc:
A:= select(filter,Primes); # Robert Israel, Jul 25 2014

Mathematica

QuadPrimes2[1, 1, 4, 1000000] (* see A106856 *)