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 A141177 #41 Jul 14 2019 17:39:03
%S A141177 3,31,37,67,97,103,157,163,181,199,223,229,313,331,367,379,397,421,
%T A141177 433,463,487,499,577,619,631,643,661,691,709,727,751,757,823,829,859,
%U A141177 883,907,991,1021,1039,1087,1093,1123,1153,1171,1213,1237,1279,1291,1303,1321,1423,1453,1483
%N A141177 Primes of the form -2*x^2 + 3*x*y + 3*y^2 (as well as of the form 4*x^2 + 7*x*y + y^2).
%C A141177 Discriminant = 33. 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 A141177 It is true that A141177(n+1) = A107013(n)? That is: except for p = 3 are these the primes represented by x^2 - x*y + 25*y^2 with x, y nonnegative? - _Juan Arias-de-Reyna_, Mar 19 2011
%C A141177 From _Jianing Song_, Jul 30 2018: (Start)
%C A141177 Also primes that are squares modulo 33.
%C A141177 Also primes of the form x^2 - x*y - 8*y^2 with 0 <= x <= y (or x^2 + x*y - 8*y^2 with x, y nonnegative).
%C A141177 These are primes = 3 or congruent to {1, 4, 16, 25, 31} mod 33. Note that the binary quadratic forms with discriminant 33 are in two classes as well as two genera, so there is one class in each genus. A141176 is in the other genus, with primes = 11 or congruent to {2, 8, 17, 29, 32} mod 33.
%C A141177 The observation from Juan Arias-de-Reyna is correct, since the binary quadratic forms with discriminant -99 are also in two classes as well as two genera. Note that -99 = 33*(-3) = (-11)*(-3)^2, so this sequence is essentially the same as A107013.
%C A141177 (End)
%D A141177 Z. I. Borevich and I. R. Shafarevich, Number Theory.
%D A141177 D. B. Zagier, Zetafunktionen und quadratische Körper: Eine Einführung in die höhere Zahlentheorie, Springer-Verlag Berlin Heidelberg, 1981, DOI 10.1007/978-3-642-61829-1.
%H A141177 Juan Arias-de-Reyna, <a href="/A141177/b141177.txt">Table of n, a(n) for n = 1..10000</a>
%H A141177 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 A141177 a(2) = 31 because we can write 31 = -2*4^2 + 3*4*3 + 3*3^2 (or 31 = 4*2^2 + 7*2*1 + 1^2).
%t A141177 Select[Prime[Range[500]], # == 3 || MatchQ[Mod[#, 33], Alternatives[1, 4, 16, 25, 31]]&] (* _Jean-François Alcover_, Oct 28 2016 *)
%Y A141177 Cf. A141176 (d=33); A038872 (d=5); A038873 (d=8); A068228, A141123 (d=12); A038883 (d=13); A038889 (d=17); A141111, A141112 (d=65).
%Y A141177 Cf. A243185 (numbers of the form -2*x^2 + 3*x*y + 3*y^2).
%Y A141177 Cf. A107013.
%Y A141177 For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.
%K A141177 nonn
%O A141177 1,1
%A A141177 Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (marcanmar(AT)alum.us.es), Jun 12 2008