# You, You and only you

Number Theory Level pending

We define a sequence $$u(n)$$ for $$n=0,1,2 ,\ldots$$ as follows: $$u(0) = 0, u(1)=1$$, and for each $$n\geq1$$, $$u(n+1)$$ is the smallest positive integer such that $$u(n+1)>u(n)$$ and $$\{u(0),u(1),u(2) ,\ldots, u(n+1)\}$$ contains no 3 elements which are in an arithmetic progression.

What is $$u (2016)$$?

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