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i stand duly chastised.
only now have i come to
figure out what your pi
conjecture even is:
does some *first* block
of n digits (1st, 2nd, ...
n^th) repeat *right away*
in digits n+1, n+2, ... 2n ?

gee. seems very unlikely.
i have no idea how one would
go about *proving* anything
like this, though ...

i think your reasoning's
a little shady on the
infinite product: it *is*
possible for an infinite
product of nonzero factors
(not "terms") to be zero.
e.g. (1/2)*(1/2)*(1/2) ...
is clearly smaller than any
positive number. your
product has the n^th factor
approaching 1 as n->\infty,
though (the condition for
an infitite product to be
interesting), so, again,
i'm with you: i don't know
how to compute its value.

anyhow, the probability that
a random normal number will
repeat its first n blocks
in positions n+1 through 2n
doesn't tell us anything
about pi itself even if
we knew pi to be normal
(which, anyway, *i* don't).

you might very well have hit
on a problem for which math
just isn't ready ...


ah yes, factors...of course. my students would laugh me out of the school if they saw that i misused the words, since i insist they use them right.

see the post for an update.

göğüs büyütücü


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