F. M. Dekking
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.
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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.
Key concepts: Natural number, Base (topology), Natural (archaeology), Mathematics, Representation (politics), Arithmetic, Combinatorics, Product (mathematics)