## Problem of the Day #335: Zeroes, Ones, and TwosFebruary 17, 2012

Posted by Albert in : potd , trackback

For how many sets $\{a_k\}_{k=0}^\infty$ of integers $0$, $1$, and $2$, does:

$$\sum\limits_{k=0}^\infty a_k 2^k$$

equal $25$? $100$? $2^n – 1$ for some positive integer $n$?