Journal of Integer Sequences, Vol. 12 (2009), Article 09.6.4

Families of Rational Numbers with Predictable Engel Product Expansions

R. S. Melham
Department of Mathematical Sciences
University of Technology, Sydney
PO Box 123, Broadway, NSW 2007


In 1987 Knopfmacher and Knopfmacher published new infinite product expansions for real numbers 0 < A < 1 and A > 1. They called these expansions Engel product expansions. At that time they had difficulty finding rational 0 < A < 1 for which the Engel product expansion is predictable. Later, in 1993, Arnold Knopfmacher presented many such families of rationals. In this paper we add to Arnold Knopfmacher's list of such families.

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Received July 9 2009; revised version received August 5 2009. Published in Journal of Integer Sequences, August 30 2009.

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