I worked on this once after an argument with my boyfriend.

The original argument was "the ones digit has permanent pattern in 2^n {2,4,8,6,2...}.

We made a system to generate digits for powers of two, although eventually we just made one that can take arbitrary bases, and found that you can decompose digit frequency and find a variety of NMR like resonances that vary based on where you terminate data collection.

It was really fun and this makes me want to get back into this so I could check the properties of those resonances across bases and stopping points for data collection.