A141304 Primes of the form -2*x^2+6*x*y+3*y^2 (as well as of the form 7*x^2+12*x*y+3*y^2).

3, 7, 43, 67, 103, 127, 163, 223, 283, 307, 367, 463, 487, 523, 547, 607, 643, 727, 787, 823, 883, 907, 967, 1063, 1087, 1123, 1303, 1327, 1423, 1447, 1483, 1543, 1567, 1627, 1663, 1723, 1747, 1783, 1867, 1987, 2083, 2143, 2203, 2287, 2347, 2383, 2467, 2503, 2647, 2683

Offset: 1

Author

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

Keywords

• nonn

Comments

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

This is also the list of primes p such that p = 3 or p is congruent to 7 or 43 mod 60. - Jean-François Alcover, Oct 28 2016

Examples

			a(3)=43 because we can write 43=-2*1^2+6*1*3+3*3^2 (or 43=7*1^2+12*1*2+3*2^2).
		

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.

Crossrefs

Cf. A107152, A141302, A141303 (d=60).

Primes in A243190.

Programs

Mathematica

Select[Prime[Range[500]], # == 3 || MatchQ[Mod[#, 60], 7|43]&] (* Jean-François Alcover, Oct 28 2016 *)