Journal of Integer Sequences, Vol. 15 (2012), Article 12.1.6 |

Department of Pure Mathematics

University of Waterloo

200 University Avenue West

Waterloo, Ontario N2L 6P1

Canada

Paul Vrbik

Department of Computer Science

University of Western Ontario

1151 Richmond Street North

London, Ontario N6A 5B7

Canada

**Abstract:**

Let **F**(*z*) = Σ_{n ≥ 1} *f*_{n} *z*^{n} 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*| < *q*^{-μ}
has infinitely many solutions (*p*,*q*)
∈ **Z** × **N**. In this paper, using a method
introduced by Bugeaud,
we prove that

μ(**F**(1/*b*)) ≤
275331112987/137522851840 = 2.002075359 ...

for all
integers *b* ≥ 2. This improves upon the previous bound of
μ(**F**(1/*b*)) ≤ 5
given by Adamczewski and Rivoal.

(Concerned with sequence A014577.)

Received September 14 2011;
revised version received December 14 2011.
Published in *Journal of Integer Sequences*, December 27 2011.

Return to