[seqfan] Re: Initial Digits of Ternary Pi

Jack Brennen jfb at brennen.net
Mon Nov 28 23:05:10 CET 2016


I'm sure somebody should double check this, but here goes...

Note that after 3n steps on a random walk, the chance that all three
random options (0,1,2) would be equally balanced is equal to:

    (3n)! / n! / n! / n! / 3^(3n)

Using Stirling's approximation, this is asymptotic to:

    sqrt(3)/(2*Pi*n)

or about 0.276/n.

That does diverge of course, so there should be an infinite
number of times that the three digits balance.

- Jack


On 11/28/2016 12:49 PM, Hans Havermann wrote:
>> I'd already checked to 8*10^9.
>
> For what it's worth, I've now checked up to 10^10 initial digits. No third term.
>
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