Correlation of the Rudin-Shapiro sequence along prime numbers
Number Theory
2023-06-21 v1
Abstract
The correlation measure of order is a measure of pseudorandomness that quantifies the similarity between a sequence and its shifts. It is known that the correlation of order 4 is large for the Rudin-Shapiro sequence despite having nice pseudorandom properties with respect to the correlation of order 2. In this paper, we prove a radically different behavior along the subsequence of prime numbers and continue the investigation towards the pseudorandomness of subsequences of automatic sequences. This result generalizes the result of Aloui, Mauduit, and Mkaouar (2021) about the correlation of the sum of digits function along prime numbers.
Keywords
Cite
@article{arxiv.2306.10629,
title = {Correlation of the Rudin-Shapiro sequence along prime numbers},
author = {Pierre Popoli},
journal= {arXiv preprint arXiv:2306.10629},
year = {2023}
}
Comments
19 pages, 1 figure