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A096873
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Minimum diameter of an integral set of n points in the plane, no 3 on a line, no 4 on a circle.
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2
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OFFSET
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1,4
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COMMENTS
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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.
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REFERENCES
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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).
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LINKS
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Table of n, a(n) for n=1..7.
Tobias Kreisel, Sascha Kurz, There are integral heptagons, no three points on a line, no four on a circle, preprint (2006)
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.
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CROSSREFS
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Cf. A007285, A096872.
Sequence in context: A001799 A205505 A058068 * A282786 A241630 A153482
Adjacent sequences: A096870 A096871 A096872 * A096874 A096875 A096876
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KEYWORD
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hard,nonn,more
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AUTHOR
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Sascha Kurz, Jul 13 2004
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EXTENSIONS
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a(7) computed in [Kreisel-Kurz].
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STATUS
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approved
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