A problem by Antony Diaz

Level pending

We have a function that \( f\left( 1 \right) =0\\ \\ f\left( 2n \right) =2\cdot f\left( n \right) +1\\ f\left( 2n+1 \right) =2\cdot f\left( n \right) \)

What is the smallest n such that \(\\ f\left( n \right) =2014\\ \\ \) ?

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