A193556 -id:A193556 - cp's OEIS frontend

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

Hugo Pfoertner, Jul 30 2011

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.

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).

A193839 Smallest possible value of the maximum of squared distances between any two out of n points with integer coordinates and distinct mutual distances.

Original entry on oeis.org

1, 5, 10, 20, 37, 50, 73, 100, 137, 185, 241, 292

Offset: 2

Hugo Pfoertner, Aug 06 2011

			Configurations minimizing the maximum distance between 2 points:
a(2)=1: ((0,0),(0,1)), dist^2={1}
a(3)=5: ((0,0),(0,1)),(1,2), dist^2={1,2,5}
a(4)=10: ((0,0),(0,1),(2,1),(3,0)), dist^2={1,2,4,5,9,10}
a(5)=20: ((0,1),(1,0),(2,4),(3,2),(3,4)), dist^2={1,2,4,5,8,10,13,17,18,20}
a(6)=37: ((0,1),(1,1),(2,2),(4,2),(4,5),(6,0)), dist^2={1,2,4,5,8,9,10,13,17,20,25,26,29,32,37}
a(7)=50: (( 0,5),(1,2),(1,4),(3,0),(3,5),(7,4),(7,5)), dist^2={1,2,4,5,8,9,10,13,16,17,20,25,32,34,36,37,40,41,45,49,50}
From _Bert Dobbelaere_, Dec 26 2019: (Start)
a(8)=73: ((0,0),(8,3),(6,6),(8,1),(6,5),(5,0),(0,3),(1,1))
a(9)=100: ((0,0),(8,6),(7,7),(5,8),(9,1),(9,0),(6,4),(0,4),(2,0))
a(10)=137: ((0,3),(11,7),(9,10),(11,3),(9,9),(5,11),(6,0),(6,2),(3,3),(1,2))
a(11)=185: ((1,0),(12,8),(7,12),(0,13),(9,10),(10,9),(4,12),(3,12),(9,3),(1,8),(1,2))
a(12)=241: ((0,1),(15,5),(8,14),(13,8),(10,9),(4,12),(7,9),(10,0),(8,0),(0,6),(2,0),(0,2))
a(13)=292: ((0,8),(16,14),(15,15),(16,6),(16,8),(13,1),(14,12),(11,0),(13,8),(7,0),(6,15),(4,4),(0,9))
(End)

Cf. A193838, A193555, A193556 configurations minimizing radius of enclosing circle.

a(10)-a(13) from Bert Dobbelaere, Dec 26 2019

cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

Links

Crossrefs

A193839 Smallest possible value of the maximum of squared distances between any two out of n points with integer coordinates and distinct mutual distances.

Views

Author

Keywords

Examples

Crossrefs

Extensions