# 4 for fort

Let $a_1$, $a_2$, $a_3$, $a_4$, $\ldots$ be a sequence of all numbers which can be expressed as sums of different non-negative integer powers of 4 (which is the form of $4^{k_1}+4^{k_2}+4^{k_3}+\ldots+4^{k_p}$, $k_m\neq k_n$, $m,n={1,2,3,\ldots,p}$, $m\neq n$ where $k$ is a non-negative integer) arranging from the smallest to the largest.

The first few terms are as follows, $a_1=4^0=1$ $a_2=4^1=4$ $a_3=4^0+4^1=5$ $a_4=4^2=16$ $a_5=4^0+4^2=17$ $\ldots$

Find the value of $a_{64}$.

Note: The $k_i$ need not to be the same for different $a_j$.

×