A problem by Antony Diaz

Level pending

We have a function that f ( 1 ) = 0 f ( 2 n ) = 2 f ( n ) + 1 f ( 2 n + 1 ) = 2 f ( n ) 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 ( n ) = 2014 \\ f\left( n \right) =2014\\ \\ ?


The answer is 2081.

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