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
USA

Abstract:

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.


Full version:  pdf,    dvi,    ps,    latex    


(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.


Return to Journal of Integer Sequences home page