On some properties of a meta-Fibonacci sequence connected to Hofstadter sequence and Möbius function. (May 2020)

• Record Type: Journal Article
• Authors: Trojovský, Pavel
• Is Part Of: Chaos, solitons and fractals. Volume 134(2020)
• Publication Date: 2020-05
• Subjects: Hofstadter Q-sequence -- Meta-sequence -- Möbius function -- Chaos -- Fractal -- Nonlinearity; 11B39; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.109708
• Languages: English
• ISSNs: 0960-0779

Abstract

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.