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Re^4: Latent Japh

by blazar (Canon)
on Oct 24, 2005 at 09:44 UTC ( #502421=note: print w/replies, xml ) Need Help??

in reply to Re^3: Latent Japh
in thread Latent Japh

I'm not a mathemagician - but I'm guessing that since pi's digits are an infinite nonrepeating sequence, then it must hold true that any other finite sequence you ever wanted to see exists somewhere in the digits of pi

No, it is not true that "it must". In fact it needs not, i.e. a number's digits being an infinite nonrepeating sequence is not an sufficient condition for it to include any given finite subsequence. Check the definition of normal number (which is itself slightly stronger than the above, involving a requirement on the limiting frequency) e.g. here. However it is indeed postulated that pi is normal, but needless to say it's extremely difficult to prove such a claim.

In this vein you guys may also be interested in the miraculous Bailey-Borwein-Plouffe formula which gives somewhat unexpectedly (and slightly simplifying) the n-th hexadecimal digit of pi independently of the previous ones, which makes it particularly suitable for distribuited computing...

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