The Josephus Problem

A puzzle with a 1st-century backstory (Josephus reportedly used it to survive) and a slick binary answer.

n people stand in a circle, numbered 1 to n. Starting the count at person 1, you go around eliminating every 2nd person (so person 2 goes first, then person 4, …) and keep looping until only one survives.

For example with n = 41 people, most seats are doomed — but exactly one is safe.

If there are 41 people, which position should you stand in to be the sole survivor?

(Answer with the seat number.)