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A096873
Minimum diameter of an integral set of n points in the plane, no 3 on a line, no 4 on a circle.
2
1, 1, 1, 8, 73, 174, 22270
OFFSET
1,4
COMMENTS
An integral set is a set where all distances between points are integers.
As of 2011, it is not known if this sequence is finite or even if a(8) exists.
REFERENCES
H. Harborth, Integral distances in point sets, Butzer, P. L. (ed.) et al., Karl der Grosse und sein Nachwirken. 1200 Jahre Kultur und Wissenschaft in Europa. Band 2: Mathematisches Wissen. Turnhout: Brepols. 213-224 (1998).
LINKS
T. Kreisel and S. Kurz, There are integral heptagons, no three points on a line, no four on a circle, Discrete and Computational Geometry 39 Issue 4 (2008), 786-790, MR2413160
J. Solymosi and F. de Zeeuw, On a Question of Erdos and Ulam, Discrete and Computational Geometry Vol. 43 Issue 2 (2010), 393-401.
CROSSREFS
Sequence in context: A001799 A205505 A058068 * A282786 A241630 A153482
KEYWORD
hard,nonn,more
AUTHOR
Sascha Kurz, Jul 13 2004
EXTENSIONS
a(7) computed in [Kreisel-Kurz].
STATUS
approved