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On Some Properties of the Hofstadter–Mertens Function

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  • Pavel Trojovský

Abstract

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 ) by , 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†.

Suggested Citation

  • Pavel Trojovský, 2020. "On Some Properties of the Hofstadter–Mertens Function," Complexity, Hindawi, vol. 2020, pages 1-6, September.
    • Handle: RePEc:hin:complx:1816756
    DOI: 10.1155/2020/1816756
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