*(This question was posted on MSE on 8. September (<https://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 $\pi$?
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> 
> 



$\pi$, disjunctive numbers, and finite sequences of given length
This is known since 2010 at least for $n\leq 11$ -- see [this entry](http://oeis.org/A036903) in the OEIS or F. Bellards's [page about digits of $\pi$](http://bellard.org/pi/pi2700e9/pidigits.html). In fact, every sequence of length $11$ occurs once in the first $2\ 512\ 258\ 603\ 207$ digits of $\pi$.


