%I #40 Oct 02 2023 16:51:25
%S 4,6,6,6,8,7,8,9,8,8,10,9,9,10,10,10,10,11,10,12,12,12,11,11,12,12,12,
%T 13,12,12,13,13,13,13,14,14,13,13,14,14,14,14,14,14,14,15,14,15,15,15,
%U 15,15,16,15,16,15,16,16,15,15,16,16,16,16,16,16,16,16,17,17,16,17,17,16,17,17
%N Maximal number of vertices of a convex lattice polygon containing n lattice points in its interior.
%C This is an inverse of A063984 in the following sense: A063984(k) = min {n : a(n)>=k}. Thus a(n) grows roughly like const*n^(1/3). - _Günter Rote_, Sep 19 2023
%H Günter Rote, <a href="/A322345/b322345.txt">Table of n, a(n) for n = 0..200</a>
%H Wouter Castryck, <a href="https://doi.org/10.1007/s00454-011-9376-2">Moving Out the Edges of a Lattice Polygon</a>, Discrete Comput. Geom., 47 (2012), p. 496-518, Column n_max in Table 1, p 512.
%H Wouter Castryck, <a href="https://homes.esat.kuleuven.be/~wcastryc/# :~:text=Moving%20out%20the%20edges%20of%20a%20lattice%20polygon">Homepage</a>. See the accompanying files for the above-referenced paper.
%H Günter Rote, <a href="/A322345/a322345.py.txt">Python program</a> for this sequence and for A298562, (2023).
%H Günter Rote, <a href="/A322345/a322345.txt">Table of n, a(n) for n = 0..200</a> together with a corresponding a(n)-gon for each n, (2023).
%o (Python) # See the Python program in the links section.
%Y Cf. A063984, A187015, A322343, A322346, A298562, A298755.
%K nonn
%O 0,1
%A _Hugo Pfoertner_, Dec 04 2018
%E a(0) added by _Andrey Zabolotskiy_, Dec 29 2021
%E Name clarified by _Günter Rote_, Sep 18 2023
%E a(31) onwards from _Günter Rote_, Oct 01 2023