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A141337
Primes of the form -2*x^2+6*x*y+7*y^2 (as well as of the form 14*x^2+22*x*y+7*y^2).
2
7, 11, 19, 23, 43, 67, 79, 83, 103, 107, 191, 199, 227, 251, 263, 283, 359, 367, 379, 383, 419, 431, 467, 479, 503, 523, 563, 571, 619, 631, 643, 659, 727, 743, 751, 787, 827, 839, 907, 911, 919, 971, 983, 1019, 1031, 1063, 1091, 1103, 1123, 1171, 1187, 1259
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(5)=43 because we can write 43=-2*10^2+6*10*3+7*3^2 (or 14*1^2+22*1*1+7*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. A141336 (d=92).
Sequence in context: A343142 A235727 A370010 * A192187 A053403 A032672
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