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Zeckendorf Representation

A number written as a sum of nonconsecutive Fibonacci Numbers,

n=\sum_{k=0}^L \epsilon_kF_k,

where $\epsilon_k$ are 0 or 1 and


Every Positive Integer can be written uniquely in such a form.

See also Zeckendorf's Theorem


Grabner, P. J.; Tichy, R. F.; Nemes, I.; and Pethö, A. ``On the Least Significant Digit of Zeckendorf Expansions.'' Fib. Quart. 34, 147-151, 1996.

Vardi, I. Computational Recreations in Mathematica. Reading, MA: Addison-Wesley, p. 40, 1991.

Zeckendorf, E. ``Représentation des nombres naturels par une somme des nombres de Fibonacci ou de nombres de Lucas.'' Bull. Soc. Roy. Sci. Liège 41, 179-182, 1972.

© 1996-9 Eric W. Weisstein