## Sum of digits sequence

### Problem 551

Let `a`_{0}, `a`_{1}, `a`_{2}, ... be an integer sequence defined by:

`a`_{0}= 1;- for
`n`≥ 1,`a`is the sum of the digits of all preceding terms._{n}

The sequence starts with 1, 1, 2, 4, 8, 16, 23, 28, 38, 49, ...

You are given `a`_{106} = 31054319.

Find `a`_{1015}.