The Audition Circle

At a mass casting call, $2020$ hopefuls stand in a circle, numbered $1$ to $2020$. The director starts at number $1$: she spares $1$, cuts $2$, spares $3$, cuts $4$, and continues around and around the shrinking circle — always sparing one person and cutting the next — until a single hopeful remains. What number gets the part?