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

Author

Hugo Pfoertner, Nov 10 2022

Keywords

• nonn

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

• 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

Crossrefs

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

Programs

Python

# See Rote link.

Extensions

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

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