A Problem on Sequence

Define a sequence \(u_n\), where \(n = 0,1,2,\ldots\) as follows: \(u_0 = 0 , u_1 = 1\), and for each \(n\geq 1\), \(u_{n+1}\) is the smallest positive integer such that \(u_{n+1} > u_{n}\) and \( \{u_{0}, u_{1},\ldots, u_{n+1} \} \) contains no three elements which are in arithmetic progression. Find \(u_{2016}\).

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