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