a_{n }exceeds 1 when n=1, 2 when n=3, 3 when n=7, 4 when n=13, and so on.
So I conjecture that the digit k is exceeded on the (k^2  k + 1)th term.
For the problem where k=2020, n= 2020^2  2020 + 1 = 4078381
I have no idea what is going on.
**Kenny M got here first.
**The answer to Jer's question would seem to be 2021^2 2021.

Posted by xdog
on 20201028 11:51:59 