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 A139492 #34 Feb 18 2022 03:52:32
%S A139492 7,37,43,67,79,109,127,151,163,193,211,277,331,337,373,379,421,457,
%T A139492 463,487,499,541,547,571,613,631,673,709,739,751,757,823,877,883,907,
%U A139492 919,967,991,1009,1033,1051,1087,1093,1117,1129,1171,1201,1213,1297,1303
%N A139492 Primes of the form x^2 + 5x*y + y^2 for x and y nonnegative.
%C A139492 Reduced form is [1, 3, -3]. Discriminant = 21. Class number = 2.
%C A139492 Values of the quadratic form are {0, 1, 3, 4} mod 6, so this is a subsequence of A002476. - _R. J. Mathar_, Jul 30 2008
%C A139492 It can be checked that the primes p of the form x^2 + n*x*y + y^2, n >= 3, where x and y are nonnegative, depend on n mod 6 as follows: n mod 6 = 0 => p mod 12 = {1,5}; n mod 6 = 1 => p mod 12 = {1,7}; n mod 6 = 2 => p mod 12 = {1}; n mod 6 = 3 => p mod 12 = {1,5,7,11}; n mod 6 = 4 => p mod 12 = {1}; n mod 6 = 5 => p mod 12 = {1,7}. - _Walter Kehowski_, Jun 01 2008
%D A139492 Z. I. Borevich and I. R. Shafarevich, Number Theory.
%D A139492 David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989.
%H A139492 Peter Luschny, <a href="https://oeis.org/wiki/User:Peter_Luschny/BinaryQuadraticForms#Implementation">Binary Quadratic Forms</a>
%H A139492 N. J. A. Sloane et al., <a href="/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a>: Index to related sequences, programs, references. OEIS wiki, June 2014.
%H A139492 D. B. Zagier, <a href="https://doi.org/10.1007/978-3-642-61829-1">Zetafunktionen und quadratische Körper</a>, Springer, 1981.
%e A139492 a(1) = 7 because we can write 7 = 1^2 + 5*1*1 + 1^2.
%t A139492 a = {}; w = 5; k = 1; Do[Do[If[PrimeQ[n^2 + w*n*m + k*m^2], AppendTo[a, n^2 + w*n*m + k*m^2]], {n, m, 400}], {m, 1, 400}]; Union[a]
%o A139492 (Sage) # uses[binaryQF]
%o A139492 # The function binaryQF is defined in the link 'Binary Quadratic Forms'.
%o A139492 Q = binaryQF([1, 5, 1])
%o A139492 print(Q.represented_positives(1303, 'prime')) # _Peter Luschny_, May 12 2021
%Y A139492 Primes in A243172.
%Y A139492 Cf. A002476, A007645, A007519, A033212, A033215, A068228, A107008, A107145, A107152, A139490, A139489, A139491, A139492, A141159.
%Y A139492 For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.
%K A139492 nonn
%O A139492 1,1
%A A139492 _Artur Jasinski_, Apr 24 2008