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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. 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 (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.

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: 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)

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

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Last modified August 22 16:37 EDT 2019. Contains 326179 sequences. (Running on oeis4.)