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 language | English |
|---|---|
| Article number | A45 |
| Pages (from-to) | 1-6 |
| Number of pages | 6 |
| Journal | Integers |
| Volume | 20 |
| Publication status | Published - 2020 |