A271490 Size of maximal subset of points of n X n grid such that no two points are at the same distance.

1, 2, 3, 4, 5, 6, 7, 7, 8, 9, 10, 10, 11, 11, 12, 13, 13

Offset: 1

Author

N. J. A. Sloane, Apr 14 2016

Keywords

• nonn
• hard
• more
• nice

Comments

Inverse function to A193838, which is the main entry for this problem.

Examples

			From _Ehit Dinesh Agarwal_, May 28 2020: (Start)
An 11 X 11 grid has only two subsets of size 10, barring symmetry: {(0,0), (0,2), (0,3), (0,7), (1,10), (5,4), (6,0), (8,7), (9,8), (10, 10)} and {(0,0), (0,6), (0,7), (1,2), (4,10), (7,8), (7,10), (9,2), (9,6), (10,5)}.
A 12 x 13 grid has only four subsets of size 11, barring symmetry: {(0,0), (0,1), (0,9), (0,12), (2,0), (5,3), (6,12), (7,0), (8,4), (10,10), (11,11)}. (End)
		

References

• R. K. Guy, Unsolved Problems in Number Theory, Third Edition, Springer New York, 2004, F2, 367-368.
• Keith F. Lynch, Posting to Math Fun Mailing List, Apr 02 2016.

Links

• P. Erdős and R. K. Guy, Distinct distances between lattice points, Elemente der Mathematik 25 (1970), 121-123.
• Wolfram Demonstration Project, No Repeated Distances
• A. Zimmermann, Al Zimmermann's Programming Contests: Point Packing. (Oct 10, 2009).

Crossrefs

Cf. A193838, A335232 (number of solutions).

Extensions

a(11)-a(13) corrected and extended by Ehit Dinesh Agarwal, May 28 2020

a(14)-a(16) from Bert Dobbelaere, Sep 20 2020

a(17) from Fausto A. C. Cariboni, Jul 16 2022