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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 (list; graph; refs; listen; history; text; internal format)



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.


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.


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




Hugo Pfoertner, Jul 30 2011



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Last modified November 28 12:20 EST 2022. Contains 358416 sequences. (Running on oeis4.)