TITLE: On Bailey–Borwein–Plouffe formula for irrational numbers
QUESTION [12 upvotes]: A BBP-type formula for an irrational number $\alpha$ in the integer base $b\geq 2$ is a formula in the form $\alpha=\Sigma_{k=0}^{\infty}\frac{1}{b^k}\frac{p(k)}{q(k)}$ ($p, q$ are polynomials in integer coefficients) that allows computing the $n$th digit of $\alpha$ in the basis $b$ directly and without any need to computing the preceding $n-1$ digits of $\alpha$. It is also connected to the problem of normality of irrational numbers. 
1- For which irrational numbers do we have a known Bailey–Borwein–Plouffe formula? For which of them do we have such a formula in the base $10$? (Please add a reference to a list if there is any). 
2- Is there any known BBP formula for $e$ in an integer base $b$? 
3- For which irrational numbers, the normality of the number in a given base is proved using a BBP formula?

REPLY [4 votes]: Concerning (1), there is a large compendium of BBP formulas in this paper by Bailey. Regarding (2), it is strongly suspected (but not proved) that there is no BBP formula for $e$.  Here is a quote from the paper by Bailey. 

Powers of $e$ are specified here because, as far as anyone can tell (although this has not
  been rigorously proven), $e$ is not a polylogarithmic constant in the sense of this paper,
  and thus it and its powers are not expected to satisfy BBP-type linear relations (this
  assumption is confirmed by extensive experience using the author’s PSLQ programs).