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.

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

Table of n, a(n) for n=2..16.

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

Adjacent sequences: A193552 A193553 A193554 * A193556 A193557 A193558

Keyword

nonn,frac,hard,more

Author

Hugo Pfoertner, Jul 30 2011

Status

approved