OFFSET
1,1
COMMENTS
Discriminant = 257. Class = 3. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d=b^2-4ac and gcd(a,b,c)=1.
REFERENCES
Z. I. Borevich and I. R. Shafarevich, Number Theory
LINKS
Juan Arias-de-Reyna, Table of n, a(n) for n = 1..10000
Peter Luschny, Binary Quadratic Forms
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(6)=197 because we can write 197 = 8*5^2+5*1-8*1^2.
MATHEMATICA
q := 8*x^2 + x*y - 8*y^2; pmax = 3000; xmax = xmax0 = 50; ymin = ymin0 = -50; ymax = ymax0 = 50; k = 1.3 (* expansion coeff. for maxima *) ; dx = dy = 2; prms0 = {}; prms = {2}; While[prms != prms0, xx = yy = {}; prms0 = prms; prms = Reap[Do[p = q; If[2 <= p <= pmax && PrimeQ[p], AppendTo[xx, x]; AppendTo[yy, y]; Sow[p]], {x, 1, If[xmax == xmax0, xmax, Floor[k*xmax]], dx}, {y, If[ymin == ymin0, ymin, Floor[k*ymin]], If[ymax == ymax0, ymax, Floor[k*ymax]]}, dy]][[2, 1]] // Union; xmax = Max[xx]; ymin = Min[yy]; ymax = Max[yy]; Print[Length[prms], " terms", " xmax = ", xmax, " ymin = ", ymin, " ymax = ", ymax ]]; A141167 = prms (* Jean-François Alcover, Oct 26 2016 *)
PROG
(Sage)
# The function binaryQF is defined in the link 'Binary Quadratic Forms'.
Q = binaryQF([8, 1, -8])
print(Q.represented_positives(2213, 'prime')) # Peter Luschny, Oct 26 2016
CROSSREFS
Numbers of the form 8x^2+xy-8y^2 in A243180.
Cf. A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141111, A141112 (d=65). A141168 (d=257).
For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.
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