On some properties of a meta-Fibonacci sequence connected to Hofstadter sequence and Möbius function. (May 2020) - Trojovský, Pavel
Highlights: Introduction the Hofstadter-Möbius sequence. Deserts in the Hofstadter-Möbius sequence. Valleys in the Hofstadter-Möbius sequence. Peaks in the Hofstadter-Möbius sequence. Abstract: The Hofstadter Q -sequence is perhaps the most known example of meta-Fibonacci sequence. Many authors have been interested in meta-Fibonacci sequences related to this sequence. For example, recently, it was studied by A. Alkan, N. Fox, and O. Aybar the connection between the Q -sequence and the Hofstadter-Conway $ 10, 000 sequence. Here, in the similar spirit as their paper, we study the interplay between the Hofstadter Q -sequence and one of the more important multiplicative arithmetic function, namely, the Möbius function.