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

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* = 3*a*+5*b*-6.

(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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