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 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. 1
 4, 9, 6, 6, 5, 6, 5, 6, 6, 6, 6 (list; graph; refs; listen; history; text; internal format)
 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 Sequence in context: A184988 A108533 A200414 * A168608 A200383 A199513 Adjacent sequences:  A248863 A248864 A248865 * A248867 A248868 A248869 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

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Last modified August 12 11:16 EDT 2020. Contains 336438 sequences. (Running on oeis4.)