How to add two natural numbers in base PHI
F. Michel Dekking (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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Abstract
In the base phi representation, any natural number is written uniquely as a sum of powers of the golden mean with coefficients 0 and 1, where it is required that the product of two consecutive digits is always 0. In this self-contained paper, we give a new and short proof of the recursive structure of the base phi representations of the natural numbers.