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sequence with sum 2018, no sum of a set of consecutive = 40, max length?

Source: Tournament of Towns, Senior O-Level , Spring 2019 p5

May 11, 2020
SequencealgebraSumpositive integers

Problem Statement

Consider a sequence of positive integers with total sum 20192019 such that no number and no sum of a set of consecutive num bers is equal to 4040. What is the greatest possible length of such a sequence?
(Alexandr Shapovalov)