On the irrationality exponent of the regular paperfolding numbers

In this paper, improving the method of Allouche et al., we calculate the Hankel determinant of the regular paperfolding sequence, and prove that the Hankel determinant sequence modulo 2 is periodic with period 10 which answers Coonʼs conjecture. Then we extend Bugeaudʼs method 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.