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On Shanks' algorithm for computing the continued fraction of log_b a
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Terence Jackson

Department of Mathematics,

University of York, Heslington

York YO105DD, England

`thj1@york.ac.uk`

and

Keith Matthews

University of Queensland

Brisbane, Australia, 4072

`krm@maths.uq.edu.au`

**Abstract:**
We give a more practical variant of Shanks' 1954 algorithm for
computing the continued fraction of log_b *a*,
for integers *a* > *b* > 1,
using the floor and ceiling functions and an integer parameter *c* > 1.
The variant, when repeated for a few values of *c* = 10^r, enables one to
guess if log_b *a* is rational and to find
approximately *r* partial quotients.

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(Concerned with sequence
A028507
.)

Received November 19, 2002;
revised version received December 6, 2002.
Published in *Journal of Integer Sequences* December 10, 2002.

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