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Weird sequence problem

Source: 2023 Japan MO Finals 3

February 11, 2023
algebra

Problem Statement

Let cc be a nonnegative integer. Find all infinite sequences of positive integers {an}n≥1\{a_{n}\}_{n\geq 1} satisfying the following condition: for all positive integer nn, there are exactly ana_n positive integers ii such that ai≤an+1+ca_i\leq a_{n+1}+c.
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