Problem

Source: Canada RepĂȘchage 2024/2 CMOQR

Tags: number theory



Call a natural number N good if its base 3 expansion has no consecutive digits that are the same. For example, 289 is good since its base 3 representation is 1012013. Find the 2024th smallest good number (0 is not considered to be a natural number). Your answer should be in base 10.