Post Closed as "off topic" by Gjergji Zaimi, Bruce Westbury, Steve Huntsman, Dmitri Pavlov, Simon Thomas
4 edited body

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 I mean the set of (k,b,f) triples, for a given base, where f is the first position of occurrence.

3 deleted 8 characters in body

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.

Curiosly if

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 occuring 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.

2 edited body
1