# Factored radix numbers

The problem:

- Four digits to sequentially index a growing collection of entities,
- a strong preference for human-friendly decimal,
- but the possibility of reaching 10000 and regret at not having chosen hexadecimal or vigesimal.

What to do?

For me, the question became theoretical, but I considered it long enough to define a numeral system, factored radix numbers (pdf), as well as a filter program to do conversions between FR and decimal.

The essence of the answer is simple:
Use decimal up to 9999.
For higher numbers, e.g., 123456,
remove a *prefix* (12) to leave the allowed
number of characters (4) in the *stem* (3456).
Then encode the prefix within the stem in a manner
somewhat analogous to digital steganography.
However, obscurity is not the goal.
Instead, make it easy to recover both the stem and the prefix -
much easier than converting base 20 to decimal.

For the details, see the article linked above.