OFFSET
1,1
COMMENTS
Discriminant = 28. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac.
Also primes of form 7*u^2-v^2. The transformation {u,v}={-x-y,3*x+2*y} yields the form in the title. [Juan Arias-de-Reyna, Mar 19 2011]
This is also the list of primes p such that p = 7 or p is congruent to 3, 19 or 27 mod 28. - Jean-François Alcover, Oct 28 2016
REFERENCES
Z. I. Borevich and I. R. Shafarevich, Number Theory.
LINKS
Juan Arias-de-Reyna, Table of n, a(n) for n = 1..10000
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS: Index to related sequences, programs, references. OEIS wiki, June 2014.
D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.
EXAMPLE
a(3)=19 because we can write 19=-2*4^2+2*4*3+3*3^2 (or 19=6*1^2+10*1*1+3*1^2).
MATHEMATICA
Select[Prime[Range[250]], # == 7 || MatchQ[Mod[#, 28], 3|19|27]&] (* Jean-François Alcover, Oct 28 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (lourdescm84(AT)hotmail.com), Jun 12 2008
STATUS
approved