On some properties of a meta-Fibonacci sequence connected to Hofstadter sequence and Möbius function

Trojovský, Pavel

doi:10.1016/j.chaos.2020.109708

Chaos, Solitons & Fractals

2020

DOI: 10.1016/j.chaos.2020.109708

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On some properties of a meta-Fibonacci sequence connected to Hofstadter sequence and Möbius function

Pavel Trojovský

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On Some Properties of the Hofstadter–Mertens Function

Trojovský

2020

Complexity

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Many mathematicians have been interested in the study of recursive sequences. Among them, a class of “chaotic” sequences are named “meta-Fibonacci sequences.” The main example of meta-Fibonacci sequence was introduced by Hofstadter, and it is called the Q-sequence. Recently, Alkan–Fox–Aybar and the author studied the pattern induced by the connection between the Q-sequence and other known sequences. Here, we continue this program by studying a “Mertens’ version” of the Hofstadter sequence, defined (for x>0) by x↦∑n≤xμnQn, where µ(n) is the Möbius function. In particular, as we shall see, this function encodes many interesting properties which relate prime numbers to “meta-sequences”.

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On Some Properties of the Hofstadter–Mertens Function

Trojovský

2020

Complexity

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On some properties of a meta-Fibonacci sequence connected to Hofstadter sequence and Möbius function

Cited by 1 publication

References 9 publications

On Some Properties of the Hofstadter–Mertens Function

On Some Properties of the Hofstadter–Mertens Function

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