A141336 Primes of the form 2*x^2+6*x*y-7*y^2 (as well as of the form 2*x^2+10*x*y+y^2).

2, 13, 29, 41, 73, 101, 173, 193, 197, 233, 257, 269, 277, 317, 349, 353, 397, 409, 449, 461, 509, 541, 577, 593, 601, 653, 673, 761, 809, 821, 829, 853, 857, 877, 929, 997, 1013, 1021, 1061, 1093, 1097, 1117, 1129, 1153, 1181, 1237, 1277, 1289, 1297, 1301

Offset

1,1

Comments

Discriminant = 92. Class = 2. 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.

D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.

Links

Table of n, a(n) for n=1..50.

Example

a(2)=13 because we can write 13=2*2^2+6*2*1-7*1^2 (or 13=2*1^2+10*1*1+1^2).

Mathematica

Reap[For[p = 2, p < 2000, p = NextPrime[p], If[FindInstance[p == 2*x^2 + 6*x*y - 7*y^2, {x, y}, Integers, 1] =!= {}, Print[p]; Sow[p]]]][[2, 1]] (* Jean-François Alcover, Oct 25 2016 *)

Crossrefs

Cf. A141337 (d=92).

Sequence in context: A042917 A366720 A174049 * A253970 A361836 A298392

Adjacent sequences: A141333 A141334 A141335 * A141337 A141338 A141339

Keyword

nonn

Author

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), Jun 25 2008

Extensions

More terms from Colin Barker, Apr 05 2015

Status

approved