The Mephisto waltz sequence is defined by beginning with 0 and then iterating the maps
and .
This gives 0, 001, 001001110, 001001110001001110110110001, ... (OEIS A064990).
These words are fourth power-free (Allouche and Shallit 2003, p. 25).
The numbers of 0s and 1s in step , 1, ... are given by 1, 2, 5, 14, 41, 122, ... (OEIS A007051) and 0, 1, 4, 13, 40, 121, ... (OEIS A003462), respectively, which are given in closed
form by
and ,
respectively.
A recurrence plot of the Mephisto waltz sequence
is illustrated above.