OFFSET
1,1
COMMENTS
Discriminant = 56. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac.
Also primes of the form x^2 + 6xy - 5y^2, cf. A243186. - N. J. A. Sloane, Jun 05 2014
REFERENCES
Z. I. Borevich and I. R. Shafarevich, Number Theory.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS: Index to related sequences, programs, references. OEIS wiki, June 2014.
D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.
EXAMPLE
a(3) = 43 is in the sequence because we can write 43 = 2*4^2 + 4*4*1 - 5*1^2, or 43 = 2*3^2 + 8*3*1 + 1^2.
MATHEMATICA
xy[{x_, y_}]:={2 x^2 + 4 x y - 5 y^2, 2 y^2 + 4 x y - 5 x^2}; Union[Select[Flatten[xy/@Subsets[Range[50], {2}]], #>0&&PrimeQ[#]&]] (* Vincenzo Librandi, Jun 09 2014 *)
CROSSREFS
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