Random challenge, probably easy:
A number is in base-b simplified Goodstein form if it is written as
b + b + ... + b + c, c ≤ b
The simplified Goodstein sequence of a number starts with writing the number in base-1 simplified Goodstein form, then replacing all 1's with 2's and subtracting 1. Rewrite the result in base-2 simplified Goodstein form, then replace all 2's with 3's and subtract 1, etc. until you reach 0. For example: If you start with 3, it looks like this.