[FOM] 770 in Pi

[David Ross]

> However, my query relates to the remark above.  It is indeed easy to
prove
> that "almost all" (in the sense of probability) reals are normal to
ALL
> bases.  Yet AFAIK there are no specific examples of such a one that is
> known for certain - actually proved so.
>
> Does anyone know of an example, or even a construction method for one?

There's an example of such an "absolutely normal" number due to
Sierpinski in 1917, but it is not obviously computable.  There have also
been some computable variants of this (I found one in a computer science
journal a few years ago, when I was teaching an upper-division
probability course, but decided not to inflict it on my students).

David Ross