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

Author

Hugo Pfoertner, Jul 30 2011

Keywords

• nonn
• frac
• hard
• more

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).