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%I #25 Feb 17 2022 11:37:37
%S 2,5,17,53,113,137,173,197,233,257,293,317,353,557,593,617,653,677,
%T 773,797,857,953,977,1013,1097,1193,1217,1277,1373,1433,1493,1553,
%U 1613,1637,1697,1733,1877,1913,1973,1997,2153,2213,2237,2273,2297,2333,2357,2393,2417,2477
%N Primes of the form 2*x^2+6*x*y-3*y^2 (as well as of the form 5*x^2+10*x*y+2*y^2).
%C Discriminant = 60. Class = 4. 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 This is also the list of primes p such that p = 2 or 5 or p is congruent to 17 or 53 mod 60. - _Jean-François Alcover_, Oct 28 2016
%D Z. I. Borevich and I. R. Shafarevich, Number Theory.
%H Juan Arias-de-Reyna, <a href="/A141303/b141303.txt">Table of n, a(n) for n = 1..10000</a>
%H 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 D. B. Zagier, <a href="https://doi.org/10.1007/978-3-642-61829-1">Zetafunktionen und quadratische Körper</a>, Springer, 1981.
%e a(3)=17 because we can write 17=2*2^2+6*2*1-3*1^2 (or 17=5*1^2+10*1*1+2*1^2).
%t Select[Prime[Range[500]], # == 2 || # == 5 || MatchQ[Mod[#, 60], 17|53]&] (* _Jean-François Alcover_, Oct 28 2016 *)
%Y Cf. A107152, A141302, A141304 (d=60).
%Y Primes in A243189.
%K nonn
%O 1,1
%A Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), Jun 24 2008
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