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A243576 Denominator of largest minimal l^1 distance for n points in the simplex x+y+z=1, 0<=x,y,z<=1. 1

%I

%S 1,1,3,1,1,5,4,3,3,5,7,15,2,2,21,13,9,9

%N Denominator of largest minimal l^1 distance for n points in the simplex x+y+z=1, 0<=x,y,z<=1.

%C a(n) is the denominator (in lowest terms) of the maximum of min(|x_i-x_j| + |y_i-y_j| + |z_i-z_j|, 1 <= i < j <= n) where x_i, y_i, z_i >= 0, x_i + y_i + z_i = 1 for 1<=i<=n.

%H Robert Israel, <a href="http://www.math.ubc.ca/~israel/packing/">A packing problem</a>

%H Robert Israel, <a href="/A243487/a243487.pdf">A packing problem</a> [Cached version, pdf format, with permission]

%H Robert Israel, <a href="https://oeis.org/A243487/a243487_3.png">Illustration for a(17), with caption</a>

%H Robert Israel, <a href="https://oeis.org/A243487/a243487_2.png">Illustration for a(17), without caption</a>

%H Math Overflow, <a href="http://mathoverflow.net/questions/168363/what-is-the-most-diverse-k-subset-of-0-1m/168476#168476">What is the most ``diverse'' k-subset of [0,1]^m?</a>

%F For n=3 an optimal configuration consists of [1,0,0],[0,1,0],[0,0,1], with all distances 2, so a(3) = 1.

%Y Numerator is A243487(n).

%K nonn,frac

%O 2,3

%A _Robert Israel_, Jun 06 2014

%E More terms from _Robert Israel_, Jun 22 2014

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Last modified March 30 05:55 EDT 2020. Contains 333119 sequences. (Running on oeis4.)