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Integers without distances 1,2,6 between them

Source: 38th Brazilian MO (2016) - Second Day - Problem 4

November 23, 2016
Brazilian Math Olympiad 2016combinatorics

Problem Statement

What is the greatest number of positive integers lesser than or equal to 2016 we can choose such that it doesn't have two of them differing by 1,2, or 6?