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
USA

Abstract:

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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