On the irrationality exponent of the regular paperfolding numbers
Abstract
In this paper, improving the method of Allouche et al. 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 CV12. Then we extend Bugeaud's method 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.
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