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
In this paper, we prove that a class of regular sequences can be viewed as projections of fixed points of uniform morphisms on a countable alphabet, and also can be generated by countable states automata. Moreover, we prove that the regularity of some regular sequences is invariant under some codings.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.