Josephus problem

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Josephus problem is a math puzzle with a grim description: $n$ prisoners are standing on a circle, sequentially numbered from $0$ to $n-1$.

An executioner walks along the circle, starting from prisoner $0$, removing every $k$-th prisoner and killing him.

As the process goes on, the circle becomes smaller and smaller, until only one prisoner remains, who is then freed.

For example, if there are $n=5$ prisoners and $k=2$, the order the prisoners are killed in (let's call it the "killing sequence") will be 1, 3, 0, and 4, and the survivor will be #2.

Given any $n, k > 0$, find out which prisoner will be the final survivor.

In one such incident, there were 41 prisoners and every 3rd prisoner was being killed ($k=3$).

Among them was a clever chap name Josephus who worked out the problem, stood at the surviving position, and lived on to tell the tale.

Which number was he?