Square-free tower of Hanoi sequences (Q1355390)

Summary: The sequence of moves in the optimal solution of the Tower of Hanoi with an arbitrary number of discs has recently been shown to lead to an example of an infinite square-free string over a six-letter alphabet by recourse to the theory of iterated morphisms. We present a direct approach to this result, using only properties of the Tower of Hanoi itself, which also reveals an implicit infinite square-free string with just five letters.