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A271490
Size of maximal subset of points of n X n grid such that no two points are at the same distance.
8
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
P. Erdős and R. K. Guy, Distinct distances between lattice points, Elemente der Mathematik 25 (1970), 121-123.
Wolfram Demonstration Project, No Repeated Distances
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
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