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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 (list; graph; refs; listen; history; text; internal format)



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.


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).


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.


Cf. A007285, A096872.

Sequence in context: A001799 A205505 A058068 * A282786 A241630 A153482

Adjacent sequences:  A096870 A096871 A096872 * A096874 A096875 A096876




Sascha Kurz, Jul 13 2004


a(7) computed in [Kreisel-Kurz].



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Last modified November 18 09:17 EST 2017. Contains 294879 sequences.