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Mephisto Waltz Sequence

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The Mephisto waltz sequence is defined by beginning with 0 and then iterating the maps 0->001 and 1->110. 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 n=0, 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 (3^n+1)/2 and (3^n-1)/2, respectively.

Mephisto waltz sequence recurrence plot

A recurrence plot of the Mephisto waltz sequence is illustrated above.

See also

Thue-Morse Sequence

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References

Allouche, J.-P. and Shallit, J. Exercise 1.9.16 in Automatic Sequences: Theory, Applications, Generalizations. Cambridge, England: Cambridge University Press, p. 25, 2003.Jacobs, K. Invitation to Mathematics. Princeton, NJ: Princeton University Press, pp. 105-106 and 215, 1992.Sloane, N. J. A. Sequences A007051/M1458, A003462/M3463, and A064990 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Mephisto Waltz Sequence

Cite this as:

Weisstein, Eric W. "Mephisto Waltz Sequence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MephistoWaltzSequence.html

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