The structure of geometric number sequences
J. V. Leyendekkers, Anthony G. Shannon · 2011
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 struct- ure in the modular rings Z3 and Z4 of some elements of these sequences reinforce previous studies of their properties.