The Parity of the Sum-of-digits-function of Generalized Zeckendorf Representations *

Abstract

with respect to basis G, where the digits si si{ji) > 0 are integers. This digital expansion is unique, when one assumes that the digits et are chosen in such a way that the digital sum Z7>! si is as small as possible; in this case, we will call the digital expansion a proper digital expansion. It is easy to see that the following algorithm provides this… (More)

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