A285521 - OEIS

A285521

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

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

(list; table; graph; refs; listen; history; text; internal format)

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.

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.

x x

Table begins:

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

Sequence in context: A318423 A318091 A301608 * A187451 A134542 A106254

Adjacent sequences: A285518 A285519 A285520 * A285522 A285523 A285524

KEYWORD

nonn,tabl

AUTHOR

Peter Kagey, Apr 20 2017

STATUS

approved