cp's OEIS Frontend

A141191 Primes of the form -2*x^2+4*x*y+5*y^2 (as well as of the form 10*x^2+16*x*y+5*y^2).

%I A141191 #22 Oct 25 2016 14:28:15
%S A141191 5,7,13,31,47,61,101,103,157,167,173,181,199,223,229,269,271,293,311,
%T A141191 349,367,383,397,439,461,479,503,509,607,647,661,677,719,727,733,773,
%U A141191 797,829,839,853,887,941,983,997,1013,1021,1039,1063,1069,1109,1151,1181
%N A141191 Primes of the form -2*x^2+4*x*y+5*y^2 (as well as of the form 10*x^2+16*x*y+5*y^2).
%C A141191 Discriminant = 56. 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.
%C A141191 Also primes of the form -x^2+6xy+5y^2. cf. A243187.
%D A141191 Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966.
%D A141191 D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.
%H A141191 N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)
%e A141191 a(4)=31 because we can write 31=-2*7^2+4*7*3+5*3^2 (or 31=10*1^2+16*1*1+5*1^2).
%t A141191 Reap[For[p = 2, p < 2000, p = NextPrime[p], If[FindInstance[p == -2*x^2 + 4*x*y + 5*y^2, {x, y}, Integers, 1] =!= {}, Print[p]; Sow[p]]]][[2, 1]] (* _Jean-François Alcover_, Oct 25 2016 *)
%Y A141191 Cf. A141190 (d=56) A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65).
%Y A141191 Cf. A243187, A243186, A141190.
%Y A141191 For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.
%K A141191 nonn
%O A141191 1,1
%A A141191 Laura Caballero Fernandez,Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (lourdescm84(AT)hotmail.com), Jun 12 2008
%E A141191 More terms from _Colin Barker_, Apr 05 2015