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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 (list; graph; refs; listen; history; text; internal format)
 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 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: A065312 A343142 A235727 * A192187 A053403 A032672 Adjacent sequences:  A141334 A141335 A141336 * A141338 A141339 A141340 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

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Last modified September 18 22:05 EDT 2021. Contains 347546 sequences. (Running on oeis4.)