## Eleven-free integers

### Problem 442

Published on Saturday, 26th October 2013, 01:00 pm; Solved by 213; Difficulty rating: 55%An integer is called *eleven-free* if its decimal expansion does not contain any substring representing a power of 11 except 1.

For example, 2404 and 13431 are eleven-free, while 911 and 4121331 are not.

Let E(*n*) be the *n*th positive eleven-free integer. For example, E(3) = 3, E(200) = 213 and E(500 000) = 531563.

Find E(10^{18}).