"Because π, like any other irrational number, contains any sequence imaginable that is fixed in advanced" -- To my knowledge, that is an open question for $\pi$; can you reference a proof? The more general claim is just straight up false; it is easy to construct irrational numbers that don't use some digits at all, e.g. $0.101001000100001...$.

@NicolaGigante Oof. Damned if I know ... thank the powers that be for the internet archive.

@theDoctor Not if you don't have _ - 1, I don't think; see the comments above. If you can prove otherwise, please add an answer!

You may want to read cs.stackexchange.com/questions/23068/…

@zgc anchor, hypothesis, and step