Let $a_0,a_1,\dots$ be an integer sequence defined by:

• $a_0=1$;
• for $n\ge 1$, $a_n$ is the sum of the digits of all preceding terms.

The sequence starts with $1,1,2,4,8,16,23,28,38,49,\dots$
You are given $a_{{10}^6}=31054319$.

Find $a_{{10}^{15}}$.