Inspired by this question, I would like to know what is the longest known sequence of consecutive zeros in Pi (in base 10).
So far the longest I have found is the sequence of 8 zero's occurring in position 172,330,850 after the decimal point.
If we expand the question to longest sequence of identical digits, 6 takes a lead with 9 digits occurring at position 45,681,781. All other digits have 8 digit maximum sequences occurring within the first 200,000,000 digits.
In general what is known about the distribution of k-length b-sequences in Pi, where b is any of the base digits? Can something be learned about the normalcy of Pi from these distributions? NB, by distribution I mean the set of (k,b,f) triples, for a given base, where f is the first position of occurrence.