login
Minimum diameter of an integral set of n points in the plane, not all on a line.
(Formerly M3295)
3

%I M3295 #32 Nov 29 2023 11:41:44

%S 1,4,7,8,17,21,29,40,51,63,74,91,104,121,134,153,164,196,212,228,244,

%T 272,288,319,332,364,396,437,464,494,524,553,578,608,642,667,692,754,

%U 816,897,959,1026,1066,1139,1190,1248,1306,1363

%N Minimum diameter of an integral set of n points in the plane, not all on a line.

%C An integral set is a set where all distances between points are integers.

%D S. Kurz and A. Wassermann, On the minimum diameter of plane integral point sets, Ars Combinatoria, Vol. 101 (2011), 265-287.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Jason Kimberley from Kurz and Laue, <a href="/A007285/b007285.txt">Table of n, a(n) for n = 3..122</a>

%H H. Harborth, A. Kemnitz, and M. Moeller, <a href="http://dx.doi.org/10.1007/BF02189331">An upper bound for the minimum diameter of integral plane sets</a>, Discr. Comput. Geom. 9 (1993), 427-432.

%H Sascha Kurz and Reinhard Laue, <a href="http://arxiv.org/abs/0804.1296">Bounds for the minimum diameter of integral point sets</a>, arXiv:0804.1296 [math.CO], 2008-2019.

%Y Cf. A096872, A096873.

%K nonn,nice

%O 3,2

%A _N. J. A. Sloane_

%E More terms from _Sascha Kurz_, Sep 11 2003

%E 396 from _Sascha Kurz_, Jul 13 2004