A little Googling told me that I should be thinking about "mixed radix number systems", "change-making problems", "coin collector's problem", "implied probability distributions", and "Fibonacci codes". The Fibonacci code is particularly interesting, since the implicit probability distribution is O(n^-1.44), which is pretty darn close to the O(n^-1.5) from theoretical & empirical grounds for cache behavior. https://en.wikipedia.org/wiki/Fibonacci_coding This coding suggests that an elegant computer cache might possibly be designed using *Fibonacci numbers*. At 08:53 AM 4/22/2018, Henry Baker wrote:
Are there any number notations that aren't *based*, in the sense that one digit doesn't represent O(1/|b|) of the next higher-order digit, where b is the "base" ?
I'm particularly looking for notations which *don't* converge quickly.
This may sound silly, but why bother with a notation that converges more quickly than series you're trying to represent?