Arbitrary Sequence of Digits in Irrational Number

Question

What are numbers in which we can find arbitrary sequence of digits (in a certain base-$n$ expansion)? I know that $0.123456789101112131415\cdots$ does (and its analogues in other bases), but does this property hold for some more familiar numbers like algebraic integers or $e$, $\gamma$ or $\pi$?

Answer 1

Nobody knows. For all we know, the decimal expansions of $\sqrt2$, $e$, and $\pi$ could all have nothing but zeros and ones from some point on.