cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A141189 Primes of the form x^2+7*x*y-y^2 (as well as of the form 7*x^2+9*x*y+y^2).

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%I A141189 #17 Oct 25 2016 14:28:41
%S A141189 7,11,13,17,29,37,43,47,53,59,89,97,107,113,131,149,163,197,199,211,
%T A141189 223,227,229,241,269,271,281,293,307,311,317,331,347,367,409,431,433,
%U A141189 439,449,461,467,487,521,523,541,547,577,587,593,599,607,619,643,647,653
%N A141189 Primes of the form x^2+7*x*y-y^2 (as well as of the form 7*x^2+9*x*y+y^2).
%C A141189 Discriminant = 53. 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.
%C A141189 A subsequence of (and may possibly coincide with) A038931. - _R. J. Mathar_, Jul 22 2008
%D A141189 Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966.
%D A141189 D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.
%H A141189 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 A141189 a(5) = 29 because we can write 29 = 3^2+7*3*1-1^2 (or 29 = 7*1^2+9*1*2+2^2).
%t A141189 Reap[For[p = 2, p < 1000, p = NextPrime[p], If[FindInstance[p == x^2 + 7*x*y - y^2, {x, y}, Integers, 1] =!= {}, Print[p]; Sow[p]]]][[2, 1]] (* _Jean-François Alcover_, Oct 25 2016 *)
%Y A141189 Cf. A038872 (d=5). A038873 (d=8). A038931, A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65).
%Y A141189 Primes in A243191.
%Y A141189 For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.
%K A141189 nonn
%O A141189 1,1
%A A141189 Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), Jun 12 2008