Atom - Æ! - To Factorial Base

Characters: Æ , !

Tags: arithmetic , math , number , array , vectorize , base

Arity: monadic

This atom is monadic, which means it takes one argument.

Functionality

Convert a number to factorial base.

Details

Starting from the right, each place value has a maximum allowed digit of 0, 1, 2, .... The place value of each digit is 0!, 1!, 2!, .... For example, 69 Æ! gives [2, 3, 1, 1, 0]. This is evaluated as 2×4! + 3×3! + 1×2! + 1×1! + 0×0! = 48 + 18 + 2 + 1 = 69.