Classes of Gap Balancing Numbers

Jeremiah Bartz; Bruce Dearden; Joel Iiams

Classes of Gap Balancing Numbers

Number Theory 2018-10-19 v1

Authors: Jeremiah Bartz , Bruce Dearden , Joel Iiams

Abstract

Gap balancing numbers are a certain generalization of balancing and cobalancing numbers that arise from studying the equation ${T(L)+T(B)=T(m)}$ where $T(i)$ is the $i$ th triangular number. In this paper, we survey early results, attempt to unify existing terminology, and extend prior findings. In addition, we further investigate the structure of classes of gap balancing numbers and related sequences, presenting new results and a conjecture regarding the number of classes based on the gap size.

Cite

@article{arxiv.1810.07895,
  title  = {Classes of Gap Balancing Numbers},
  author = {Jeremiah Bartz and Bruce Dearden and Joel Iiams},
  journal= {arXiv preprint arXiv:1810.07895},
  year   = {2018}
}

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14 pages

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