How to calculate the sum of digits of $2^n$? How do I find the sum of digits of $2^n$ in general?
Sum of digits of $2^1=2$ is $2$.
Sum of digits of $2^{10}=1024$ is $7$.
I have check there is no obvious pattern or any recurrence that i can find. Any ideas?
** i don't need repeated sums , just single time** 

$2^{1} = 2$
$2^{2} = 4$
$2^{3} = 8$
$2^{4} = 16 \rightarrow 7$
$2^{5} = 32 \rightarrow 5$
$2^{6} = 64 \rightarrow 10 \rightarrow 1$
Then..
$2^{7} = 128 \rightarrow 11 \rightarrow 2$
$2^{8} = 256 \rightarrow 13 \rightarrow 4$
$2^{9} = 512 \rightarrow 8$
$2^{10} = 1024 \rightarrow 7$
$2^{11} = 2048 \rightarrow 14 \rightarrow 5$
$2^{12} = 4096 \rightarrow 19 \rightarrow 10 \rightarrow 1$
If you keep this up, it seems you will find that
$2^{n} \equiv 2^{n+6}$
when summing the digits of the result of each.
