I'm looking for a succint phrase to describe the set of numbers
$$S_b = \{i\in\mathbb{Z}: b^i\}. $$
That is, the numbers which are all powers of a (specific) common base $b$.
I've played with "exponent-b numbers", "base-b power" numbers, etc. but they don't seem to fit.
For example, consider units of computer memory, where the total number of bytes is typically an exponent of 2. I'd like to say something more succinct than "on systems with memory that is an exponent of 2, you get...". For instance, "on systems with base-2 memory".
What's a sensible phrase to use here? Do such sets of numbers have a particular name?
Simplest one would be just the "Powers of B" or "B-Powers". Otherwise "Exponent Set of B", "Set of Powers of B". I wouldn't recommend using the "Power Set of B" as it already has a different meaning in set theory.