OFFSET
1,1
COMMENTS
Discriminant = 61. Class = 1. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac.
A subsequence of (and may possibly coincide with) A038941. - R. J. Mathar, Jul 22 2008
3*x^2+5*x*y-3*y^2 and 5*x^2+9*x*y+y^2 are equivalent forms.
Also, primes of the form x^2 - 61y^2, of discriminant 244.
REFERENCES
Z. I. Borevich and I. R. Shafarevich, Number Theory.
LINKS
Robert Israel, 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(8) = 73 because we can write 73 = 3*4^2+5*4*5-3*5^2 (or 73 = 5*3^2+9*3*1+1^2).
MAPLE
select(p -> isprime(p) and nops([isolve(x^2 - 61*y^2 = p)])>0, [seq(2*i+1, i=1..1000)]); # Robert Israel, Jun 11 2014
MATHEMATICA
terms = 100; d = 61;
Table[3*x^2 + 5*x*y - 3*y^2, {x, 1, terms}, {y, Floor[(5 - Sqrt[d])*x/6], Ceiling[(5 + Sqrt[d])*x/6]}] // Flatten // Select[#, Positive[#] && PrimeQ[#]&]& // Union // Take[#, terms]& (* Jean-François Alcover, Feb 28 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (sergarmor(AT)yahoo.es), Jun 14 2008
STATUS
approved