OFFSET
1,6
COMMENTS
"Minimum height" means that there is no other sequence such that the convex hull is an n-gon and max(a'(1),...,a'(n)) - min(a'(1),...,a'(n)) is smaller.
Each number appears at most twice in any given row.
Conjecture: Even-length rows have rotational symmetry.
Conjecture: The maximum value in any even-length row is the same as the maximum value in the preceding row.
Conjecture by Peter Kagey: 24th row is 12, 14, 8, 17, 5, 4, 21, 22, 2, 23, 1, 1, 24, 24, 2, 23, 3, 4, 21, 20, 8, 17, 11, 13. - Lars Blomberg, May 06 2017
LINKS
Peter Kagey and Lars Blomberg, Table of n, a(n) for n = 1..276 (23 rows, first 21 rows from Peter Kagey)
Mathematics Stack Exchange user Smylic, The minimum "height" of a convex polygon on N^2.
EXAMPLE
Row 7 is [1,3,1,4,4,2,3], the lexicographically earliest sequence with the minimal height of 3 and a convex hull that forms a heptagon.
xx
x x
x
x x
Row 8 is [2,3,1,1,4,4,2,3], the lexicographically earliest sequence with the minimal height of 3 and a convex hull that forms an octagon.
xx
x x
x x
xx
Table begins:
1;
1, 1;
1, 1, 2;
1, 1, 2, 2;
1, 1, 3, 2, 3;
1, 2, 1, 3, 2, 3;
1, 3, 1, 4, 4, 2, 3;
2, 3, 1, 1, 4, 4, 2, 3;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Kagey, Apr 20 2017
STATUS
approved