Problem

Source: IMO ShortList 1998, number theory problem 4

Tags: number theory, Integer sequence, Calculate, IMO Shortlist



A sequence of integers $ a_{1},a_{2},a_{3},\ldots$ is defined as follows: $ a_{1} = 1$ and for $ n\geq 1$, $ a_{n + 1}$ is the smallest integer greater than $ a_{n}$ such that $ a_{i} + a_{j}\neq 3a_{k}$ for any $ i,j$ and $ k$ in $ \{1,2,3,\ldots ,n + 1\}$, not necessarily distinct. Determine $ a_{1998}$.


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