[poizan42]

Exactly. A number with the property that every sequence occurs is called a rich or disjunctive number - a number can be rich in s specific bases or rich for all bases we don't know whether pi is any if that. A number where every sequence occurs equally often (scaled to the length of the sequence) is called a normal number, which is an even stronger property.

[sponaugle]

While Pi is not proven to be a disjunctive number, nor the stronger condition of being normal, it is generally believed to be normal. That being said we don't have a proof of Pi being normal, nor disjunctive.

I am not familiar with how a proof of that would be constructed, as clearly numerical or computational measurements could never be conclusive.