A141785 Primes of the form -x^2 + 5*x*y + 5*y^2 (as well as of the form 9*x^2 + 15*x*y + 5*y^2).

5, 11, 29, 41, 59, 71, 89, 101, 131, 149, 179, 191, 239, 251, 269, 281, 311, 359, 389, 401, 419, 431, 449, 461, 479, 491, 509, 521, 569, 599, 641, 659, 701, 719, 761, 809, 821, 839, 881, 911, 929, 941, 971, 1019, 1031, 1049, 1061, 1091, 1109, 1151, 1181, 1229, 1259

Offset: 1

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

Keywords

• nonn

Comments

Discriminant = 45. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac.

Examples

			a(2) = 29 because we can write 29 = -1^2 + 5*1*2 + 5*2^2 (or 29 = 9*1^2 + 15*1*1 + 5*1^2)
		

References

• Z. I. Borevich and I. R. Shafarevich, Number Theory.

Links

• Juan Arias-de-Reyna, 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. OEIS wiki, June 2014.
• D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.

Crossrefs

Cf. A033212 (d=45), A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17): A141111, A141112 (d=65).

For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.

Programs

Mathematica

Select[Prime[Range[250]], # == 5 || MatchQ[Mod[#, 45], Alternatives[11, 14, 26, 29, 41, 44]]&] (* Jean-François Alcover, Oct 28 2016 *)