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good naturals in base 3

Source: Canada Repêchage 2024/2 CMOQR

March 25, 2024
number theory

Problem Statement

Call a natural number NN good if its base 33 expansion has no consecutive digits that are the same. For example, 289289 is good since its base 33 representation is 10120131012013. Find the 20242024th smallest good number (00 is not considered to be a natural number). Your answer should be in base 1010.
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