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Part of 2018 Federal Competition For Advanced Students, P2

Problems(1)

2018 numbers on a circle, labeled with an integer, > sum of 2 preceding, max

Source: 49th Austrian Mathematical Olympiad National Competition (Final Round, part 2) 1st June 2018 p5

5/25/2019
On a circle 20182018 points are marked. Each of these points is labeled with an integer. Let each number be larger than the sum of the preceding two numbers in clockwise order. Determine the maximal number of positive integers that can occur in such a configuration of 20182018 integers.
(Proposed by Walther Janous)
combinatoricsnumber theory