OFFSET
1,1
COMMENTS
Discriminant = 37. Class = 1. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d=b^2-4ac and gcd(a,b,c)=1
REFERENCES
Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966.
LINKS
Jean-François Alcover, Table of n, a(n) for n = 1..10000
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)
D. B. Zagier, Zetafunktionen und quadratische Körper, Springer-Verlag Berlin Heidelberg, 1981.
EXAMPLE
a(3) = 11 because we can write 11 = 3*2^2+2*1-3*1^2 (or 11 = 3*1^2+7*1*1+1^2).
MATHEMATICA
Reap[For[p = 2, p < 1000, p = NextPrime[p], If[FindInstance[p == 3*x^2 + x*y - 3*y^2, {x, y}, Integers, 1] =!= {}, Print[p]; Sow[p]]]][[2, 1]]
(* or: *)
Select[Prime[Range[200]], # == 37 || MatchQ[Mod[#, 37], Alternatives[1, 3, 4, 7, 9, 10, 11, 12, 16, 21, 25, 26, 27, 28, 30, 33, 34, 36]]&](* Jean-François Alcover, Oct 25 2016, updated Oct 30 2016 *)
CROSSREFS
Cf. A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17): A141111, A141112 (d=65).
Primes in A035267.
A subsequence of (and may possibly coincide with) A038913. - R. J. Mathar, Jul 22 2008
For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.
KEYWORD
nonn
AUTHOR
Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (marcanmar(AT)alum.us.es), Jun 12 2008
STATUS
approved