(This question was posted on MSE on 8. September (http://math.stackexchange.com/questions/487729https://math.stackexchange.com/questions/487729) but got no answer so far; hence the posting on MO.)
It is an open problem whether the number $\pi$ is disjunctive in base $10$, i.e., whether every finite sequence appears (at least once) in the base $10$ expansion of $\pi$. Of course, every sequence of length $1$ appears, and it is readily checked that so does every sequence of length $2$. A quick search on the internet turns out that this also holds for sequences of length at most $7$. I guess this can be easily checked for other small lengths, and has surely been done before. So, my question is the following:
For which natural numbers $n$ is it known that every sequence of length $n$ appears in the base $10$ expansion of $\pi$?
