Infinities of random sequences exist that can be shown not to contain all data, 0-8 (base 10) is one such random sequence that is trivially proven to never contain 9...

There are no known patterns to pi, but, (I am legitimately curious about this), are there any known sequences e.g. of 1 million 0s and a single other digit within the decimal sequence of pi?

Given how it (pi) looks, I'm of the strong suspicion is that the answer is "no". But of course, proving that requires that some property of the randomness is provable. Which it does feel as if, given there are different infinities, there are also different randomnesses, hence the conjecture is ill-formed and probably incorrect...