Given an integer , there is a smallest base for which the number has the most fours in its representations among all bases. Consider the function that gives such a base for .

Saturday Morning Breakfast Cereal calls this the "fouriest base" [1], and considers the act of moving from one base to another with more fours to be a "fourier transform".

This Demonstration calculates the fouriest base for all numbers less than a certain limit. Often is the fouriest base for .