Question

Let \(N = \sum_{k = 1}^{1000}k(\lceil \log_{\sqrt {2}}k\rceil - \lfloor \log_{\sqrt {2}}k \rfloor). \)
Find \(N\).

I put in 500497 because apparently it equals k from 3-1000 (so just 3+4+...+ 1000) but its wrong.