## zeckendorf(N)

Version 1.1.0.0 (1.95 KB) by
zeckendorf(N) using a greedy algorithm with binary exponentiation for computing Fib(n)

Updated 8 Jun 2018

Zeckendorf's theorem states that any positive integer, N, can be written as a sum of non-consecutive Fibonacci numbers uniquely. This is achieved by a greedy algorithm: the representation always starts with the largest Fibonacci number <= N.

Here, I used the definition of Fibonacci numbers as:
F(0) = 0
F(1) = 1
F(n) = F(n-1) + F(n-2).

For example: N = 100 = 89 + 8 + 3.

This code outputs the Zeckendorf representation of a positive integer N. Fibonacci numbers are computed using binary exponentiation of the Fibonacci matrix [1 1; 1 0].

### Cite As

Karl Ezra Pilario (2023). zeckendorf(N) (https://www.mathworks.com/matlabcentral/fileexchange/67017-zeckendorf-n), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2017a
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Version Published Release Notes
1.1.0.0

Added a bit string representation output.

1.0.0.0

Updated the description.