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.
%I A141161 #38 Feb 17 2022 11:36:27
%S A141161 3,7,11,41,47,53,71,73,83,101,127,149,157,173,181,197,211,223,229,263,
%T A141161 271,307,337,359,373,379,397,419,433,443,509,521,571,593,599,613,617,
%U A141161 619,641,659,673,677,719,733,739,743,751,761,773,787,811,821,887,937
%N A141161 Primes of the form 4*x^2+6*x*y-7*y^2.
%C A141161 Discriminant = 148. Class = 3. 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 A141161 Also primes represented by the improperly equivalent form 7*x^2 + 6*x*y - 4*y^2
%D A141161 Z. I. Borevich and I. R. Shafarevich, Number Theory.
%H A141161 Juan Arias-de-Reyna, <a href="/A141161/b141161.txt">Table of n, a(n) for n = 1..10000</a>
%H A141161 Peter Luschny, <a href="https://oeis.org/wiki/User:Peter_Luschny/BinaryQuadraticForms#Implementation">Binary Quadratic Forms</a>
%H A141161 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. OEIS wiki, June 2014.
%H A141161 D. B. Zagier, <a href="https://doi.org/10.1007/978-3-642-61829-1">Zetafunktionen und quadratische Körper</a>, Springer, 1981.
%e A141161 a(8)=73 because we can write 73= 4*4^2+6*4*3-7*3^2.
%t A141161 q := 4*x^2 + 6*x*y - 7*y^2; pmax = 1000; xmax = 100; ymin = -xmax; ymax = xmax; k = 1; prms0 = {}; prms = {2}; While[prms != prms0, xx = yy = {}; prms0 = prms; prms = Reap[Do[p = q; If[2 <= p <= pmax && PrimeQ[p], AppendTo[xx, x]; AppendTo[yy, y]; Sow[p]], {x, 1, k*xmax}, {y, k*ymin, k*ymax}]][[2, 1]] // Union; xmax = Max[xx]; ymin = Min[yy]; ymax = Max[yy]; k++; Print["k = ", k, " xmax = ", xmax, " ymin = ", ymin, " ymax = ", ymax ]]; A141161 = prms (* _Jean-François Alcover_, Oct 26 2016 *)
%o A141161 (Sage)
%o A141161 # The function binaryQF is defined in the link 'Binary Quadratic Forms'.
%o A141161 Q = binaryQF([4, 6, -7])
%o A141161 Q.represented_positives(937, 'prime') # _Peter Luschny_, Oct 26 2016
%Y A141161 Cf. A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65). A141163 (d=148).
%Y A141161 For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.
%K A141161 nonn
%O A141161 1,1
%A A141161 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