Definition:Zeckendorf Representation

Definition
Zeckendorf representation is a system for representing a positive integer $m$ by a sequence of digits which are the indices of a sequence of $r$ Fibonacci numbers:


 * $n := k_1 k_2 k_3 \ldots k_r$

where:
 * $n = F_{k_1} + F_{k_2} + F_{k_3} + \cdots + F_{k_r}$
 * $k_1 \gg k_2 \gg k_3 \gg \cdots \gg k_r \gg 0$

where $n \gg k$ denotes that $n \ge k + 2$.

Also known as
Some sources give this as the Fibonacci number system.

Also see

 * Zeckendorf's Theorem