If a particular constant contains every single possible combination of numbers in it's decimal expansion, does it also contain itself?

Question

If a particular constant $a$ contains every single combination of numbers in it's decimal expansion, does it then imply that at one point the series should also contain itself?

Answer 1

Suppose it contains itself, starting at the $n+1$th significant digit.
Then it also contains itself starting at the $2n+1$th significant digit. The second occurrence has the third occurrence, in the same place the first occurrence has the second occurrence - delayed by $n$ digits.
So it repeats every $n$ digits. So it contains only $n$ different $n$-digit numbers, which is a contradiction.