Comment by kadoban
https://en.wikipedia.org/wiki/Normal_number has some examples and a bunch of info. Most of them are pretty artificial, but the concatenation of the primes one is... at least interesting, not obvious (to me) from doing that that it'd be normal.
Hmm, you are referring to rich numbers but pointing to normal numbers, so I will be the nerd who points out that every normal number is rich, but some rich numbers aren't normal.
https://en.wikipedia.org/wiki/Disjunctive_sequence