The structure of geometric number sequences

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 17, 2011, Number 3, Pages 31–37
Full paper (PDF, 50 Kb)

Details

Authors and affiliations

J. V. Leyendekkers

Faculty of Science, The University of Sydney
Sydney, NSW 2006, Australia

A. G. Shannon

Faculty of Engineering & IT, University of Technology
Sydney, NSW 2007, Australia

Abstract

An integer structure analysis (ISA) of the triangular, tetrahedral, pentagonal and pyramidal numbers is developed. The relationships among the elements and the powers of the elements of these sequences are discussed. In particular, the triangular and pentagonal numbers are directly linked and are structurally important for the formation of triples. The class structure in the modular rings Z₃ and Z₄ of some elements of these sequences reinforce previous studies of their properties.

Keywords

• Integer structure analysis
• Modular rings
• Prime numbers
• Triangular numbers
• Pentagonal numbers.
• Octagonal numbers
• Repunits

AMS Classification

• 11A41
• 11A07

References

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