

A285521


Table read by rows: the nth row gives the lexicographically earliest sequence of length n such that the convex hull of (1, a(1)), ..., (n, a(n)) is an ngon with minimum height.


2



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, 1, 3, 4, 1, 5, 5, 2, 4, 3, 3, 2, 4, 1, 1, 5, 5, 2, 4, 3, 2, 1, 5, 6, 1, 7, 7, 2, 6, 3, 4, 4, 3, 6, 2, 7, 7, 1, 1, 6, 2, 5, 4, 2, 4, 1, 7, 8, 1, 9, 9, 2
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OFFSET

1,6


COMMENTS

"Minimum height" means that there is no other sequence such that the convex hull is an ngon and max(a'(1),...,a'(n))  min(a'(1),...,a'(n)) is smaller.
Each number appears at most twice in any given row.
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
Conjecture: Evenlength rows have rotational symmetry.
Conjecture: The maximum value in any evenlength 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)
Math 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 an septagon.
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 octogon.
xx
x x
x x
xx


CROSSREFS

Sequence in context: A318423 A318091 A301608 * A187451 A134542 A106254
Adjacent sequences: A285518 A285519 A285520 * A285522 A285523 A285524


KEYWORD

nonn,tabl,more


AUTHOR

Peter Kagey, Apr 20 2017


STATUS

approved



