# If $d(n)$ is the sum of digits of n, find $d(d(d(n)))$ of $n=4444^{4444}$ [duplicate]

If $d(n)$ is the sum of digits of n, find $d(d(d(n)))$ of $n=4444^{4444}$.

My attempt:

$4444^{4444}<10000^{4444}$

Now, $\max d(10000^{4444})<9\times 17776$

Again, $\max d(159984)\le 45$

Again $\max d(45)\le 12$

So, $\max d(d(d(n)))\le 12$.