Safe spot in a circle of 2000 with every second removed

Two thousand people stand in a circle numbered $1$ to $2000$. Person $1$ eliminates person $2$ and passes the sword to person $3$, who eliminates person $4$ and passes it on, and so on around the circle, each holder removing the next living person and handing the sword to the following survivor. Which numbered position is the last one remaining?

Position $1953$. This is the Josephus problem with step 2: writing $N=2^m+r$ with $0\le r<2^m$, the survivor is $2r+1$. Here $2000=1024+976$, so the survivor is $2\cdot976+1=1953$.