On Some Properties of the Hofstadter-Mertens Function

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F20%3A50017164" target="_blank" >RIV/62690094:18470/20:50017164 - isvavai.cz</a>
Result on the web
<a href="https://www.hindawi.com/journals/complexity/2020/1816756/" target="_blank" >https://www.hindawi.com/journals/complexity/2020/1816756/</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1155/2020/1816756" target="_blank" >10.1155/2020/1816756</a>

Result language
angličtina
Original language name
On Some Properties of the Hofstadter-Mertens Function
Original language description
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 ->Sigma(n <= x)mu(n)Q(n), where mu(n) is the Mobius function. In particular, as we shall see, this function encodes many interesting properties which relate prime numbers to "meta-sequences".
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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