Saturday Morning Breakfast Cereal Fourier Transform

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 .


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[1] Z. Weinersmith, Saturday Morning Breakfast Cereal (blog). (Sep 8, 2016)
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