Sum of digits of $12345$ is $1+2+3+4+5=15$. The sum of digits of sum of digits is $1+5=6$.
I have plotted the sum of digits of powers of $12345$ with blue dots (x-axis is the power).
As the average digit is $4.5$, we can see the roughly linear rise with slope $log_{10}(12345) * 4.5 ≈ 18.4$
The red dots represent the sum of digits of sum of digits. Any hint why they are multiplies of $9$? (except the first red dot with value of $6$)
Best Answer
As $12345$ is a multiple of $3$, the powers of $12345$, excluding itself, will be multiples of $9$. By the divisibility rule of $9$ the sum of the digits, and the sum of the sum of the digits will also be divisible by $9$. (That is why the first dot alone was an exception).