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URL: https://oeis.org/A141336

⇱ A141336 - OEIS

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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
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.
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
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