2011 AMC 12A Problem 19

At a competition with N players, the number of players given elite status is equal to 2^{1+\lfloor \log_{2} (N-1) \rfloor}-N. Suppose that 19 players are given elite status. What is the sum of the two smallest possible values of N?

\textbf{(A)}\ 38 \qquad \textbf{(B)}\ 90 \qquad \textbf{(C)}\ 154 \qquad \textbf{(D)}\ 406 \qquad \textbf{(E)}\ 1024

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.