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 A141302 Primes of the form -x^2+6*x*y+6*y^2 (as well as of the form 11*x^2+18*x*y+6*y^2). 10
 11, 59, 71, 131, 179, 191, 239, 251, 311, 359, 419, 431, 479, 491, 599, 659, 719, 839, 911, 971, 1019, 1031, 1091, 1151, 1259, 1319, 1439, 1451, 1499, 1511, 1559, 1571, 1619, 1811, 1871, 1931, 1979, 2039, 2099, 2111, 2339, 2351, 2399, 2411, 2459, 2531, 2579, 2591, 2699, 2711 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Discriminant = 60. Class = 4. 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 N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references) EXAMPLE a(3)=71 because we can write 71=-1^2+6*1*3+6*3^2 (or 71=11*1^2+18*1*2+6*2^2). MATHEMATICA Reap[For[p = 2, p < 3000, p = NextPrime[p], If[FindInstance[p == -x^2 + 6*x*y + 6*y^2, {x, y}, Integers, 1] =!= {}, Print[p]; Sow[p]]]][[2, 1]] (* Jean-François Alcover, Oct 25 2016 *) CROSSREFS Cf. A107152, A141303, A141304 (d=60). Primes in A237606. Sequence in context: A290360 A073720 A257364 * A139872 A165977 A214151 Adjacent sequences:  A141299 A141300 A141301 * A141303 A141304 A141305 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 24 2008 STATUS approved

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Last modified April 21 07:12 EDT 2021. Contains 343146 sequences. (Running on oeis4.)