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 A141187 Primes of the form -x^2+6*x*y+3*y^2 (as well as of the form 8*x^2+12*x*y+3*y^2). 7
 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 = 48. 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. Values of the quadratic form are {0,3,8,11} mod 12, so all values with the exception of 3 are also in A068231. - R. J. Mathar, Jul 30 2008 Is this the same sequence (apart from the initial 3) as A068231? 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)=23 because we can write 23= -1^2+6*1*2+3*2^2 (or 23=8*1^2+12*1*1+3*1^2). MATHEMATICA Reap[For[p = 2, p < 2000, p = NextPrime[p], If[FindInstance[p == -x^2 + 6*x*y + 3*y^2, {x, y}, Integers, 1] =!= {}, Print[p]; Sow[p]]]][[2, 1]] (* Jean-François Alcover, Oct 25 2016 *) CROSSREFS Cf. A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65). A068228 (d=48). Cf. A243169. 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: A078723 A294368 A296556 * A107138 A145473 A335677 Adjacent sequences:  A141184 A141185 A141186 * A141188 A141189 A141190 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 12 2008 EXTENSIONS More terms from Colin Barker, Apr 05 2015 STATUS approved

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Last modified June 22 07:09 EDT 2021. Contains 345374 sequences. (Running on oeis4.)