  A positive integer $N$ is \emph{palindromic in the base $b$} when $N =
\sum_{i=0}^{k} c_i b^i$, $c_k\neq 0$,and $c_i=c_{k-i},\; i=0,1,2,...,k$,
Focusing on powers of 2, we investigate the smallest base $b$ when $N=2^n$ is
palindromic in the base $b$.
