Problem 551
Sum of digits sequence
Let a0, a1, a2, … be an integer sequence defined by:
- a0 = 1;
- for n ≥ 1, an 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 a106 = 31054319.
Find a1015.
数字和序列
a0, a1, a2, … 是按如下方式定义的整数序列：
- a0 = 1；
- 对于n ≥ 1，an是其之前所有项的数字和。
序列一开始的几项是1, 1, 2, 4, 8, 16, 23, 28, 38, 49, …
已知a106 = 31054319。
求a1015。