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Zeckendorf Representations Using Negative Fibonacci Numbers, M W. Bunder
Zeckendorf Representations Using Negative Fibonacci Numbers, M W. Bunder
Faculty of Engineering and Information Sciences - Papers: Part A
It is well known that every positive integer can be represented uniquely as a sum of distinct, nonconsecutive Fibonacci numbers (see, e.g., Brown [1]. This representation is called the Zeckendorf representation of the positive integer. Other Zeckendorf-type representations where the Fibonacci numbers are not necessarily consecutive are possible. Brown [2] considers one where a maximal number of distinct Fibonacci numbers are used rather than a minimal number.
The Zeckendorf Representation And The Golden Sequence, Martin Bunder, Keith Tognetti
The Zeckendorf Representation And The Golden Sequence, Martin Bunder, Keith Tognetti
Faculty of Engineering and Information Sciences - Papers: Part A
The Zeckendorf representation of a number is simply the representation of that number as the sum of distinct Fibonacci numbers. If the number of terms of this sum is minimized, that representation is unique, as also is the representation when the number of terms is maximized.