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A Stoneham Number

 Published on Sunday, 25th October 2020, 10:00 am; Solved by 387;
Difficulty rating: 20%

Problem 731

$$A=\sum_{i=1}^{\infty} \frac{1}{3^i 10^{3^i}}$$

Define $A(n)$ to be the 10 decimal digits from the $n$th digit onward. For example, $A(100) = 4938271604$ and $A(10^8)=2584642393$.

Find $A(10^{16})$