A197123 Data field size...
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Jeff Sponaugle
Sep 4, 2026, 9:33:24 PMSep 4
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I was able to find the next entry for A197123 (https://oeis.org/A197123), which is the longest known repeating number in the decimal digits of Pi. I had previously found a(19)-a(23), and Jonas found a(24), and now I have found a(25).
It has been a really interesting computational problem, since you have to keep track of every unique 25 digit sequence in up to 10 trillion digits which is of course 10 trillion numbers. I used a segmented bloom filter to reduce the candidate pool into 10 pools based on the starting digit, and then a second multi-threaded prefilter and hash search to find the particular canditate that matched. I was able to use a cluster of systems in my home lab that each have 3TBs of RAM which makes the large bloom filter possible.
In this case a(25) = 2420215682379102240706463
It has been a really interesting computational problem, since you have to keep track of every unique 25 digit sequence in up to 10 trillion digits which is of course 10 trillion numbers. I used a segmented bloom filter to reduce the candidate pool into 10 pools based on the starting digit, and then a second multi-threaded prefilter and hash search to find the particular canditate that matched. I was able to use a cluster of systems in my home lab that each have 3TBs of RAM which makes the large bloom filter possible.
In this case a(25) = 2420215682379102240706463
at positions 399,369,008,413 and 2,564,331,708,881
I have the a(26) search started, but that will take quite a bit longer as I have to partition into 100 partitions to keep the bloom filter excess rates low enough, and of course I also had to compute 20T digits of Pi first.
In any case, I did the edit to add the number, but of course the data field ends up being longer than 260 characters. (it already was with a(24)). In the case of a sequence like this with a limited known sequence is that ok, or should that last entry only be in a b-file?
Cheers!
I have the a(26) search started, but that will take quite a bit longer as I have to partition into 100 partitions to keep the bloom filter excess rates low enough, and of course I also had to compute 20T digits of Pi first.
In any case, I did the edit to add the number, but of course the data field ends up being longer than 260 characters. (it already was with a(24)). In the case of a sequence like this with a limited known sequence is that ok, or should that last entry only be in a b-file?
Cheers!
-Jeff Sponaugle
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