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MathNet 2020 — Math Olympiad Vault — Part 06 Question 9

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 06

Question 9

Given an integer $n\gt 1$, perform the following operation: if $n$ is even, divide it by 2; if it is odd, add 5. If the resulting number is 1, stop; otherwise repeat the same operation indefinitely. Determine all starting values $n$ for which the process is finite, that is, eventually reaches 1.