TY - JOUR
A2 - Paun, Viorel-Puiu
AU - TrojovskÃ½, Pavel
PY - 2020
DA - 2020/09/15
TI - On Some Properties of the Hofstadterâ€“Mertens Function
SP - 1816756
VL - 2020
AB - 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”.
SN - 1076-2787
UR - https://doi.org/10.1155/2020/1816756
DO - 10.1155/2020/1816756
JF - Complexity
PB - Hindawi
KW -
ER -