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 A142957 Primes of the form 3*x^2+5*x*y-6*y^2 (as well as of the form 6*x^2+11*x*y+y^2). 0
 2, 3, 11, 31, 43, 47, 53, 61, 73, 79, 89, 97, 101, 103, 109, 113, 151, 163, 167, 191, 193, 197, 227, 229, 241, 269, 283, 293, 307, 313, 353, 379, 389, 397, 419, 421, 431, 449, 461, 463, 467, 479, 487, 491, 503, 509, 521, 547, 557, 571, 593, 607, 613, 617, 631 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Discriminant = 97. Class = 1. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d=b^2-4ac and gcd(a,b,c)=1. Is this the same as A038987? - R. J. Mathar, Oct 12 2013 Comment by Don Reble, Oct 06 2014 (Start): G. B. Mathews ("Theory of Numbers" by Chelsea publishing) might have an answer to the relation with A038987. In point 59 on page 65 he claims that - if X is a non-residue of a discriminant of a quadratic form, then X is not representable; and - if X is a residue of D, then there is a quadratic form of determinant D which represents X. If all forms of discriminant 97 are equivalent, then that might suffice. (Indeed, either +97 or -97 has class number 1; but I am not sure which sign matters, A003656 vs. A003173.) (End) REFERENCES Z. I. Borevich and I. R. Shafarevich, Number Theory. D. B. Zagier, Zetafunktionen und quadratische Koerper. LINKS EXAMPLE a(6)=47 because we can write 47=3*11^2+5*11*(-4)-6*(-4)^2 (or 47=6*2^2+11*2*1+1^2). CROSSREFS Cf. A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65). Sequence in context: A278209 A195732 A038987 * A191058 A080155 A235625 Adjacent sequences:  A142954 A142955 A142956 * A142958 A142959 A142960 KEYWORD nonn AUTHOR Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (laucabfer(AT)alum.us.es), Jul 17 2008 STATUS approved

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Last modified April 7 01:11 EDT 2020. Contains 333291 sequences. (Running on oeis4.)