Here's a random idea from a thoughtful commenter on my blog.
They had a look at this:
https://www.solipsys.co.uk/new/PowersOfTwoInLexOrder.html
And they idly wondered if it has a connection with Benford's Law:
https://en.wikipedia.org/wiki/Benford%27s_law
My first reaction is no, but then again, there's a log/exp thing going on in each case, so I'm just wondering.
Thoughts?