What is the direct formula for the following variation of Josephus problem?
There are $n$ persons, numbered $1$ to $n$, around a circle.. Starting from $k$-th person, every second person is eliminated. Given the $n$ and $k$, determine the index of the $x$-th person who is eliminated.
ADDED:In the first step the $k+1$th is eliminated.For n = 16,k = 6, elimination={7,9,...}
Thanks