Problem #90

The Cantor ternary function, F : [0,1] -> [0,1] is defined as follows:

  1. Express x in base 3. If possible, use no 1s. (This makes a difference only if the expansion ends in 022222... = 100000... or 200000... = 122222...)
  2. Replace the first 1 with a 2 and everything after it with 0.
  3. Replace all 2s with 1s.
  4. Interpret the result as a binary number. The result is F(x).

A graph of the Cantor function is shown below.

This month's problem is to evaluate

For n = 1,2, and 3. Can you find a formula for arbitrary n?

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