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 A141123 Primes of the form -x^2+2*x*y+2*y^2 (as well as of the form 3*x^2+6*x*y+2*y^2). 42
 2, 3, 11, 23, 47, 59, 71, 83, 107, 131, 167, 179, 191, 227, 239, 251, 263, 311, 347, 359, 383, 419, 431, 443, 467, 479, 491, 503, 563, 587, 599, 647, 659, 683, 719, 743, 827, 839, 863, 887, 911, 947, 971, 983, 1019, 1031, 1091, 1103, 1151, 1163, 1187, 1223 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Discriminant = 12. 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 N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references) EXAMPLE a(3) = 11 because we can write 11 = -1^2 + 2*1*2 + 2*2^2 (or 11 = 3*1^2 + 6*1*1 + 2*1^2). MATHEMATICA Reap[For[p = 2, p < 2000, p = NextPrime[p], If[FindInstance[p == -x^2 + 2*x*y + 2*y^2, {x, y}, Integers, 1] =!= {}, Print[p]; Sow[p]]]][[2, 1]] (* or: *) Select[Prime[Range[200]], # == 2 || # == 3 || Mod[#, 12] == 11&] (* Jean-François Alcover, Oct 25 2016, updated Oct 29 2016 *) CROSSREFS Cf. A068228 (d = 12), A068231 (Primes congruent to 11 (mod 12)), A141111, A141112 (d = 65). For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link. Cf. A084917. Sequence in context: A158017 A091310 A040994 * A263729 A246496 A119641 Adjacent sequences:  A141120 A141121 A141122 * A141124 A141125 A141126 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 05 2008 EXTENSIONS More terms from Colin Barker, Apr 05 2015 STATUS approved

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Last modified June 26 10:12 EDT 2019. Contains 324375 sequences. (Running on oeis4.)