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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.

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Results from first 200,000,000 digits were found using: angio.net/pi/piquery.html. –  Halfdan Faber Apr 24 '11 at 22:30
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This is not an interesting question. An interesting question is one that has the property that other people will learn something from the answer. What have I learned from the fact that the sequence "00000000" occurs somewhere between the $10^8$-th and $10^9$-th digit of $\pi$?... –  André Henriques Apr 24 '11 at 22:32
    
Well, if the position of first occurence for a k-length sentence grows at the same rate for all base digits, something can be learned from that. If 6-sequences of k length actually always occur first, then Pi would not be normal (I realize this is more than exceedingly unlikely to be the case, but would like to see some references). –  Halfdan Faber Apr 24 '11 at 22:38
    
@Halfdan: I completely agree with you. But there's only a finite amount of information that one can explore by computer. And, after that, one is still infinitely far away from infinity... –  André Henriques Apr 24 '11 at 22:53
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Ok. I have learned something from the answer: I've learned about the existence of Fabrice Belard's web page. –  André Henriques Apr 24 '11 at 22:56
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1 Answer

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There is a sequence of 12 zeroes starting at position 1755524129973; There is a sequence of 13 eights starting at position 2164164669332. You can see more statistics in Fabrice Belard's web pages.

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@Julian: Thx, much. This is excellent! Here is another link:ja0hxv.calico.jp/pai/estatistics5t.html. Thanks much to Alex Yee for providing this. They found 13 zeros in positions 3,186,699,229,890 and 3,675,091,769,442. Since this is from the longest Pi calculation done so far, this is likely the longest known zero sequence. See also: numberworld.org/misc_runs/pi-5t/announce_en.html. –  Halfdan Faber Apr 25 '11 at 1:56
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