Journal of Integer Sequences, Vol. 10 (2007), Article 07.10.4

On Some Properties of Two Simultaneous Polygonal Sequences

Joseph C. Su
P. O. Box 710
Alhambra, CA 91802


This paper focuses on the properties of integers that are simultaneously representable as both m-gonal and n-gonal numbers. Employing hyperbolic geometry, we ascertain both lower and upper bounds on these numbers when there is a finite set of these integers. We then consider the fundamental class of solutions to a generalized Pell-Diophantine equation that relates to these integers, and derive a fast algorithm that can be used to generate them.

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(Concerned with sequences A000217 A000290 A000326 A000384 A014979 A046194 and A129654 .)

Received July 25 2007; revised version received December 30 2007. Published in Journal of Integer Sequences, December 30 2007.

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