OFFSET
3,1
COMMENTS
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.
It is conjectured that the sequence has an infinite repetition of only two integers.
LINKS
Gordon Hamilton, Unsolved K-12: Grade 8 Problems
Hiroaki Yamanouchi, examples for a(3)-a(13)
EXAMPLE
a(3) = 4 because 3 points can be chosen so the minimal triangle has area 2:
.x.
...
x.x
a(6) = 6 because 3 points can be chosen so the minimal triangle has area 3:
..x..x
......
x.....
.....x
......
x..x..
a(8) is greater than or equal to 4 because of this non-optimal arrangement:
.....x.x
........
x.x.....
........
........
x.x.....
........
.....x.x
a(8) = 6 because 3 points can be chosen so the minimal triangle has area 3:
..x..x..
........
x......x
........
........
x......x
........
..x..x..
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gordon Hamilton, Mar 04 2015
EXTENSIONS
a(5), a(7) and a(9) corrected and a(10)-a(13) added by Hiroaki Yamanouchi, Mar 09 2015
STATUS
approved