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Hofstadter Male-Female Sequences


Hofstadter male-female sequence binary plot

The pair of sequences defined by F(0)=1, M(0)=0, and

F(n)=n-M(F(n-1))
(1)
M(n)=n-F(M(n-1)).
(2)

The first few terms of the "male" sequence M(n) for n=0, 1, ... are 0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, ... (OEIS A005379), and of the "female" sequence F(n) are 1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, ... (OEIS A005378).


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References

Hofstadter, D. R. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Vintage Books, p. 137, 1989.Sloane, N. J. A. Sequences A005378/M0263 and A005379/M0278 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Hofstadter Male-Female Sequences

Cite this as:

Weisstein, Eric W. "Hofstadter Male-Female Sequences." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HofstadterMale-FemaleSequences.html

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