Let a function f: N → N be defined by f(n)= [2 n, n=2,4,6,8, …; n-1, n=3,7,11,15, …; (n+1)/2, n=1,5,9,13, … then, f is

Let a function $\displaystyle f: \mathbb{N} \rightarrow \mathbb{N}$ be defined by $$f(n)=\left[\begin{array}{ll} 2 n, & n=2,4,6,8, \ldots \\ n-1, & n=3,7,11,15, \ldots \\ \frac{n+1}{2}, & n=1,5,9,13, \ldots \end{array}\right. $$ then, $\displaystyle f$ is