OFFSET

1,3

COMMENTS

In Hurwitz and Kritikos (HK) a definite form a*x^2 + 2*b*x*y + c*y^2, denoted by f(a,b,c), has discriminant Delta = -D = b^2 - 4*a*c < 0. Usually this is F = [a,2*b,c] with discriminant Disc = 4*(b^2 - a*c) = 4*Delta. A definite form is reduced if 2*|b| <= a <= c, and if any of the inequalities reduces to an equality then b >= 0 (HK, p. 179). The positive definite case has a > 0 and c > 0. Here the forms F do not need to satisfy gcd(a,2*b,c) = 1. - Wolfdieter Lang, Mar 31 2019

REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 360.

A. Hurwitz and N. Kritikos, transl. with add. material by W . C. Schulz, "Lectures on Number Theory", Springer-Verlag, New York, 1986, p. 186.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

EXAMPLE

a(5) = 2 because the two forms F = [a,2*b,c] with discriminant Disc = -4*5 = -20 are [1,0,5] and [2,2,3]. ([2,-2,3] is not reduced, (-2,2,-3) is not positive definite). - Wolfdieter Lang, Mar 31 2019

CROSSREFS

KEYWORD

nonn,nice,easy

AUTHOR

EXTENSIONS

Name clarified by Wolfdieter Lang, Mar 31 2019

STATUS

approved