cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A248866 Discrete Heilbronn Triangle Problem: a(n) is twice the maximal area of the smallest triangle defined by three vertices that are a subset of n points on an n X n square lattice.

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%I A248866 #22 Mar 13 2015 15:14:59
%S A248866 4,9,6,6,5,6,5,6,6,6,6
%N A248866 Discrete Heilbronn Triangle Problem: a(n) is twice the maximal area of the smallest triangle defined by three vertices that are a subset of n points on an n X n square lattice.
%C A248866 For n points in an n X n square, find the three points that make the triangle with minimal area. a(n) is double the maximal area of this triangle.
%C A248866 It is conjectured that the sequence has an infinite repetition of only two integers.
%H A248866 Gordon Hamilton, <a href="http://youtu.be/rz5Ap8YnWoo">Unsolved K-12: Grade 8 Problems</a>
%H A248866 Hiroaki Yamanouchi, <a href="/A248866/a248866.txt">examples for a(3)-a(13)</a>
%e A248866 a(3) = 4 because 3 points can be chosen so the minimal triangle has area 2:
%e A248866 .x.
%e A248866 ...
%e A248866 x.x
%e A248866 a(6) = 6 because 3 points can be chosen so the minimal triangle has area 3:
%e A248866 ..x..x
%e A248866 ......
%e A248866 x.....
%e A248866 .....x
%e A248866 ......
%e A248866 x..x..
%e A248866 a(8) is greater than or equal to 4 because of this non-optimal arrangement:
%e A248866 .....x.x
%e A248866 ........
%e A248866 x.x.....
%e A248866 ........
%e A248866 ........
%e A248866 x.x.....
%e A248866 ........
%e A248866 .....x.x
%e A248866 a(8) = 6 because 3 points can be chosen so the minimal triangle has area 3:
%e A248866 ..x..x..
%e A248866 ........
%e A248866 x......x
%e A248866 ........
%e A248866 ........
%e A248866 x......x
%e A248866 ........
%e A248866 ..x..x..
%K A248866 nonn,more
%O A248866 3,1
%A A248866 _Gordon Hamilton_, Mar 04 2015
%E A248866 a(5), a(7) and a(9) corrected and a(10)-a(13) added by _Hiroaki Yamanouchi_, Mar 09 2015