A139499 Primes of the form x^2 + 19x*y + y^2 for x and y nonnegative.

43, 67, 127, 151, 331, 373, 421, 457, 463, 613, 631, 739, 757, 883, 919, 967, 1033, 1087, 1171, 1327, 1381, 1429, 1453, 1471, 1549, 1579, 1597, 1747, 1759, 1789, 1801, 2053, 2083, 2143, 2269, 2293, 2311, 2347, 2389, 2473, 2503, 2671, 2767, 2797, 2857

Offset

1,1

Links

Table of n, a(n) for n=1..45.

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Mathematica

a = {}; w = 19; k = 1; Do[Do[If[PrimeQ[n^2 + w*n*m + k*m^2], AppendTo[a, n^2 + w*n*m + k*m^2]], {n, m, 400}], {m, 1, 400}]; Union[a] (*Artur Jasinski*)
upto=3000; With[{max=Ceiling[Sqrt[upto]]}, Select[Union[Select[(First[#]^2+ 19First[#]Last[#]+ Last[#]^2)&/@(Tuples[Range[0, max], {2}]), PrimeQ]], #<+upto&]] (* Harvey P. Dale, Jul 20 2011 *)

Crossrefs

Cf. A139489, A007645, A068228, A007519, A033212, A033212, A107152, A107008, A033215, A107145, A139490, A139491.

Sequence in context: A039385 A043208 A043988 * A201688 A174022 A033229

Adjacent sequences: A139496 A139497 A139498 * A139500 A139501 A139502

Keyword

nonn

Author

Artur Jasinski, Apr 24 2008

Status

approved