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

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

Offset

2,2

Links

Table of n, a(n) for n=2..13.

Example

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)

Crossrefs

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

Sequence in context: A117518 A107486 A210677 * A323831 A020714 A146523

Adjacent sequences: A193836 A193837 A193838 * A193840 A193841 A193842

Keyword

nonn,hard,more

Author

Hugo Pfoertner, Aug 06 2011

Extensions

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

Status

approved