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PreprintarXiv licencearXiv

Consecutive Cycle Sums

  • Jessica Marotti
  • Jonathan Needleman
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Abstract

Consider placing the numbers 1, …, n consecutively around an n-cycle. We ask for a given n, which numbers k can be written as a sum of consecutive numbers on the n-cycle. If all numbers between $1$ and Tn, the nth triangular number, can be written as a sum this way we say the n-cycle is complete. Our main result shows that for n≥ 8, n-cycles are incomplete.

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Cite

BibTeXRIS
BibTeX
@misc{marotti2026consecutive,
  title = {{Consecutive Cycle Sums}},
  author = {Jessica Marotti and Jonathan Needleman},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08889},
  eprint = {2610.08889},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08889},
}
RIS
TY  - UNPB
TI  - Consecutive Cycle Sums
AU  - Jessica Marotti
AU  - Jonathan Needleman
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08889
UR  - https://arxiv.org/abs/2610.08889
AB  - Consider placing the numbers 1, …, n consecutively around an n-cycle. We ask for a given n, which numbers k can be written as a sum of consecutive numbers on the n-cycle. If all numbers between $1$ and T_n, the nth triangular number, can be written as a sum this way we say the n-cycle is complete. Our main result shows that for n≥ 8, n-cycles are incomplete.
ER  -