Zeckendorf Representation

A number written as a sum of nonconsecutive Fibonacci numbers,

where  are 0 or 1 and

Every positive integer can be written uniquely in such a form.

REFERENCES:

Fraenkel, A. S. "Systems of Numeration." Amer. Math. Monthly 92, 105-114, 1985.

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

Graham, R. L.; Knuth, D. E.; and Patashnik, O. Concrete Mathematics: A Foundation for Computer Science, 2nd ed. Reading, MA: Addison-Wesley, pp. 295-296, 1994.

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.