Journal of Integer Sequences, Vol. 11 (2008), Article 08.3.3

Complementary Equations and Wythoff Sequences

Clark Kimberling
Department of Mathematics
University of Evansville
1800 Lincoln Avenue
Evansville, IN 47722


The lower Wythoff sequence a = (a(n)) and upper Wythoff sequence b = (b(n)) are solutions of many complementary equations f(a,b) = 0. Typically, f(a,b) involves composites such as a(a(n)) and a(b(n)), and each such sequence is treated as a binary word (e.g., aa and ab). Conversely, each word represents a sequence and, as such, is a linear combination of a, b, and 1, in which the coefficients of a and b are consecutive Fibonacci numbers. For example, baba = 3a+5b-6.

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(Concerned with sequences A000201 A001950 A003622 A003623 A035336 A035337 A035338 A035513 A101864 A134859 A134860 A134861 A134862 A134863 and A134864 .)

Received November 27 2007; revised version received July 21 2008. Published in Journal of Integer Sequences, August 3 2008.

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