1,1

Also primes of the form x^2+2*x*y-2*y^2.

Also primes of the form x^2+6*x*y-3*y^2.

Also primes of the form 4*x^2+8*x*y+y^2.

x^2+2*x*y-2*y^2 has discriminant = 12. 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

Is this the same as A068228? - Artur Jasinski, Jun 09 2008

Values of the quadratic form are {0,1,4,6,9,10} mod 12, so this is certainly a subset of A068228. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 30 2008

Contribution from Tito Piezas III (tpiezas(AT)gmail.com), Dec 28 2008: (Start)

Also primes of the form u^2-3v^2. The transformation {u,v} = {x+2y,y} transforms it into the form in the title.

(End)

Borevich and Shafaewich, Number Theory.

D. B. Zagier, Zetafunktionen und quadratische Koerper.

a(1)=13 because we can write 13=3^2+2*3*1-2*1^2 (or 13=1^2+4*1*2+2^2)

f[x_, y_]:=x^2+4*x*y+y^2; lst={}; Do[Do[p=f[x, y]; If[PrimeQ[p]&&p>0, AppendTo[lst, p]], {y, -4!, 3*4!}], {x, -4!, 3*4!}]; Take[Union[lst], 90] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 30 2009]

Cf. A141123 (d=12), A068228 (Primes congruent to 1 (mod 12)) A141111, A141112 (d=65).

Cf. A141187 (d=48) A038872 (d=5). A141131 (d=8). A141122, A141123 (d=12). A038883 (d=13). A038889 (d=17): A141111, A141112 (d=65).

Sequence in context: A140112 A089030 A068228 this_sequence A031339 A034938 A139530

Adjacent sequences: A141119 A141120 A141121 this_sequence A141123 A141124 A141125

nonn

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), Jun 05 2008

Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 26 2008 at the suggestion of Michael Somos.

More terms from Frank Marcoline (fvmarcoline(AT)gmail.com), Dec 12 2008