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 A141183 Primes of the form -x^2+6*x*y+2*y^2 (as well as of the form 7*x^2+10*x*y+2*y^2). 8
 2, 7, 11, 19, 43, 79, 83, 107, 127, 131, 139, 151, 167, 211, 227, 239, 263, 271, 283, 307, 347, 359, 431, 439, 479, 491, 503, 523, 547, 563, 571, 607, 659, 739, 743, 787, 811, 827, 887, 919, 967, 1019, 1031, 1051, 1063, 1091, 1151, 1163, 1187, 1223, 1231, 1283, 1319, 1327 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Discriminant = 44. 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. Also primes of form 11*u^2-v^2. The transformation {u,v}={-3*x-y,10*x+3*y} yields the form in the title. - Juan Arias-de-Reyna Mar 20 2011. Also primes p equal -1 mod 4 and = 1, 3, 4, 5, or 9  mod 11. - Juan Arias-de-Reyna Mar 20 2011. REFERENCES Z. I. Borevich and I. R. Shafarevich, Number Theory, Academic Press, NY, 1966. D. B. Zagier, Zetafunktionen und quadratische Koerper LINKS Juan Arias-de-Reyna, Table of n, a(n) for n = 1..10000 N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references) EXAMPLE a(4)=19 because we can write 19= -1^2+6*1*2+2*2^2 (or 19=7*1^2+10*1*1+2*1^2). MATHEMATICA Select[Prime[Range[250]], # == 2 || # == 11 || MatchQ[Mod[#, 44], Alternatives[7, 19, 35, 39, 43]]&] (* Jean-François Alcover, Oct 28 2016 *) CROSSREFS Cf. A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65). A141182 (d=44). For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link. Sequence in context: A106905 A097159 A139603 * A308724 A103182 A160698 Adjacent sequences:  A141180 A141181 A141182 * A141184 A141185 A141186 KEYWORD nonn AUTHOR Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (sergarmor(AT)yahoo.es), Jun 13 2008 STATUS approved

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Last modified April 5 03:58 EDT 2020. Contains 333238 sequences. (Running on oeis4.)