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551. Sum of digits sequence

Let a₀, a₁, a₂, ... be an integer sequence defined by:

• a₀ = 1;
• for n ≥ 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, ...
You are given a_10⁶ = 31054319.

Find a_10¹⁵.