OFFSET
1,1
COMMENTS
Discriminant = 229. Class = 3. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d = b^2-4ac. They can represent primes only if gcd(a,b,c)=1. [Edited by M. F. Hasler, Jan 27 2016]
Appears to be the complement of A141165 in A268155, primes that are squares mod 229. - M. F. Hasler, Jan 27 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(2)=53 because we can write 53= 3^2+15*3*1-1^2
MATHEMATICA
lim = 100; Rest@ Union@ Abs@ Flatten@ Table[x^2 + 15 x y - y^2, {x, lim}, {y, lim}] /. n_ /; CompositeQ@ n -> Nothing (* Michael De Vlieger, Jan 27 2016 *)
PROG
(PARI) is_A141166(p)=qfbsolve(Qfb(1, 15, -1), p) \\ Returns nonzero (actually, a solution [x, y]) iff p is a member of the sequence. For efficiency it is assumed that p is prime. Example usage: select(is_A141166, primes(500)) - M. F. Hasler, Jan 27 2016
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 12 2008
STATUS
approved