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

1,2

Comments

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

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

Table of n, a(n) for n=1..17.

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).

Example

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)

Crossrefs

Cf. A193838, A335232 (number of solutions).

Sequence in context: A100721 A337979 A265359 * A252649 A095703 A101041

Adjacent sequences: A271487 A271488 A271489 * A271491 A271492 A271493

Keyword

nonn,hard,more,nice

Author

N. J. A. Sloane, Apr 14 2016

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

Status

approved