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

摘要

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 $ 10,00 0 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 Mobius function. (C) 2020 Elsevier Ltd. All rights reserved.