IMO Shortlist 1998 problem N4


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2. travnja 2012.
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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}.
Izvor: Međunarodna matematička olimpijada, shortlist 1998