An Irrationality Measure for Regular Paperfolding Numbers
Department of Pure Mathematics
University of Waterloo
200 University Avenue West
Waterloo, Ontario N2L 6P1
Department of Computer Science
University of Western Ontario
1151 Richmond Street North
London, Ontario N6A 5B7
) = Σn ≥ 1 fn zn
be the generating series
of the regular paperfolding sequence. For a real number α the
irrationality exponent μ(α), of α, is defined as the
supremum of the set of real numbers μ such that the inequality
|α - p
| < q-μ
has infinitely many solutions (p
. In this paper, using a method
introduced by Bugeaud,
we prove that
275331112987/137522851840 = 2.002075359 ...
integers b ≥ 2. This improves upon the previous bound of
μ(F(1/b)) ≤ 5
given by Adamczewski and Rivoal.
Full version: pdf,
(Concerned with sequence
Received September 14 2011;
revised version received December 14 2011.
Published in Journal of Integer Sequences, December 27 2011.
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