[FOM] Wittgenstein's '770' in pi

[Timothy Y. Chow]

On Sun, 22 Jul 2007, joeshipman at aol.com wrote:
> Do the details of this method suggest any hope for a proof that pi is 
> normal to base 2?

Let x_0 = 0 and let x_n be the fractional part of

16 x_{n-1} + (120n^2 - 89n + 16)/(512n^4 - 1024n^3 + 712n^2 - 206n + 21)

Then the BBP work shows that pi is normal to base sixteen (and hence to 
base two) if and only if the sequence {x_n} is equidistributed in the unit 
interval.

While this may not seem to be an improvement, this general approach has 
succeeded in showing that certain numbers are normal to certain bases (not 
any "glamorous" numbers like pi, though).

Tim