The sum of digits function of the base phi expansion of the natural numbers

Michel Dekking*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
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Abstract

In the base phi expansion any natural number is written uniquely as a sum of powers of the golden mean with digits 0 and 1, where one requires that the product of two consecutive digits is always 0. In this paper we show that the sum of digits function modulo 2 of these expansions is a morphic sequence. In particular we prove that — like for the Thue-Morse sequence — the frequency of 0’s and 1’s in this sequence is equal to 1/2.

Original languageEnglish
Article numberA45
Pages (from-to)1-6
Number of pages6
JournalIntegers
Volume20
Publication statusPublished - 2020

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