Journal of Integer Sequences, Vol. 5 (2002), Article 02.2.7

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

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.

(Concerned with sequence A028507 .)

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