login
A193555
Numerators of the squared radii of the smallest enclosing circles of n points with integer coordinates and distinct mutual distances, arranged such that the radius of their enclosing circle is minimized. Denominators are given in A193556.
2
1, 5, 5, 5, 5365, 205, 1885, 117925, 3445, 97, 2225, 62530, 284345, 461, 146605
OFFSET
2,2
COMMENTS
Finding optimal solutions of this problem has been the topic of a round of Al Zimmermann's programming contests from July to October 2009, entitled "Point Packing".
Conjectured next terms are a(17)/A193556(17)=19720/121, a(18)/A193556(18)=5002/25.
LINKS
P. Erdős and R. K. Guy, Distinct distances between lattice points, Elemente der Mathematik 25 (1970), 121-123.
H. Lefmann and T. Thiele, Point sets with distinct distances, Serie B Informatik, B 94-16, 1994.
H. Lefmann and T. Thiele, Point sets with distinct distances, Combinatorica (1995) 15: 379.
CROSSREFS
Cf. A193556 (corresponding denominators), A193839.
Cf. A193838 (similar problem for smallest enclosing square).
Sequence in context: A092519 A198585 A224093 * A161981 A346962 A258072
KEYWORD
nonn,frac,hard,more
AUTHOR
Hugo Pfoertner, Jul 30 2011
STATUS
approved