Consider Josephus Problem, where $n$ people are placed clockwise around a circle, from 1, 2, ..., to $n$, $n$ is next to 1; every second person is eliminated each step (so the first few eliminated are 2, 4, 6, ...), until the last one, say $k$, is remained, we denote $J(n) = k$. $\forall n > 1, n \in N$, Which of the followings are true?