A357888 a(n) is the minimal squared length of the longest side of a strictly convex grid n-gon of smallest area.

2, 1, 2, 2, 5, 2, 5, 5, 5, 5, 10, 5, 10, 5, 13, 10, 13, 10, 13, 13, 17, 13, 17, 13, 25, 17, 25, 17, 25, 13, 25, 17, 26, 17, 26, 17, 26, 17, 26, 25, 26, 25, 29, 29, 29, 34, 34, 34, 41, 37, 41, 37, 41, 34, 41, 41, 41, 41, 41, 41, 61, 41, 61, 41, 61, 41, 61, 41, 41

Offset

3,1

Comments

It is conjectured that at least one polygon of smallest area exists with 4 sides of length 1 for n >= 8 and additionally 4 sides of squared length 2 for n >= 12.

Links

Table of n, a(n) for n=3..71.

Code Golf StackExchange, The smallest area of a convex grid polygon, fastest-code challenge, started by Peter Kagey, Oct 22 2022.

User AlephAlpha in Code Golf StackExchange, The smallest area of a convex grid polygon (n=7 .. 37), results of computations, Nov 2022.

Hugo Pfoertner, Illustrations of optimal polygons for n <= 26 (2018).

Günter Rote, Python program

Prog

(Python) See links

Crossrefs

Cf. A063984, A070911, A089187, A321693, A322029, A322345, A322348.

Sequence in context: A050315 A128978 A325110 * A145862 A364536 A058701

Adjacent sequences: A357885 A357886 A357887 * A357889 A357890 A357891

Keyword

nonn

Author

Hugo Pfoertner, Nov 10 2022

Extensions

a(29)-a(60) from Günter Rote, Sep 20 2023

Terms a(61) and beyond from Andrey Zabolotskiy, Sep 21 2023

Status

approved