On Some Properties of the Hofstadter–Mertens Function
Keyword(s):
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”.
1987 ◽
Vol 101
(2)
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pp. 221-231
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1990 ◽
Vol 42
(2)
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pp. 185-189
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2015 ◽
Vol DMTCS Proceedings, 27th...
(Proceedings)
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2019 ◽
Vol 16
(2)
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pp. 377-401
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