If $n$ is even, then $n+1$ is obtained from $n$ in binary by changing the final 0 to a 1; thus $f(n+1)=f(n)+1$. If $n$ is odd, then $n+1$ is obtained by changing the last 0 to a 1, the ensuing string of 1's to 0's, and then changing the next rightmost 0 to a 1. This produces no net change in the number of 1's iff $n$ ends in 01 in base 2. Thus, $f(n+1)=f(n)$ if and only if $n$ is congruent to $1 \bmod 4$, and there are 501 such numbers in the specified range.