# Powers of 2 which are Sum of Distinct Powers of 3

The powers of $2$ which are sums of distinct powers of $3$ are:
 $\displaystyle 2^0$ $=$ $\, \displaystyle 1 \,$ $\, \displaystyle =\,$ $\displaystyle 3^0$ $\displaystyle 2^2$ $=$ $\, \displaystyle 4 \,$ $\, \displaystyle =\,$ $\displaystyle 3^0 + 3^1$ $\displaystyle 2^8$ $=$ $\, \displaystyle 256 \,$ $\, \displaystyle =\,$ $\displaystyle 3^0 + 3^1 + 3^2 + 3^5$