On the irrationality exponent of the regular paperfolding numbers
Number Theory
2014-06-02 v1
Abstract
In this paper, improving the method of Allouche \emph{et al.} \cite{APWW98}, we calculate the Hankel determinant of the regular paperfolding sequence, and prove that the Hankel determinant sequence module 2 is periodic with period 10 which answers Coon's conjecture \cite{CV12}. Then we extend Bugeaud's method \cite{Bugeaud11} to obatin the exact value of the irrationality exponent for some general transcendental numbers. Using the results above, we prove that the irrationality exponents of the regular paperfolding numbers are exactly 2.
Keywords
Cite
@article{arxiv.1310.2138,
title = {On the irrationality exponent of the regular paperfolding numbers},
author = {Yingjun Guo and Wen Wu and Zhixiong Wen},
journal= {arXiv preprint arXiv:1310.2138},
year = {2014}
}