Sum the factorials of a number's digits over and over and see where the chain settles.
A digit-factorial chain replaces a number with the sum of the factorials of its digits,
then repeats. A factorion is a number that equals that sum of its own digit factorials,
so the chain stays put. Other numbers either fall onto a factorion or settle into a repeating cycle.
Example: 145 = 1! + 4! + 5! = 1 + 24 + 120 = 145, so 145 is a factorion. In base 10 there are exactly four
factorions: 1, 2, 145, and 40585.