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Counterexamples to a conjecture of Kamenetsky on OEIS A173419

  • Rosario Patanè
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Abstract

Define a(n) as the number corresponding to the shortest computation using only addition, subtraction, or multiplication, as A173419 states on the related OEIS page. In a comment to the sequence, D. Kamenetsky conjectured that a(p) ≥ a(p -1) for every prime. We show that the conjecture is false through four counterexamples below 5000 that satisfy the condition a(p) < a(p -1). They are exactly 3359, 3623, 4909, and 4943.

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Cite

BibTeXRIS
BibTeX
@misc{patane2026counterexamples,
  title = {{Counterexamples to a conjecture of Kamenetsky on OEIS A173419}},
  author = {Rosario Patanè},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28512},
  eprint = {2609.28512},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05756029v1},
}
RIS
TY  - UNPB
TI  - Counterexamples to a conjecture of Kamenetsky on OEIS A173419
AU  - Rosario Patanè
PY  - 2026
DA  - 2026/09/20
PB  - HAL
DO  - 10.48550/arxiv.2609.28512
UR  - https://hal.science/hal-05756029v1
AB  - Define a(n) as the number corresponding to the shortest computation using only addition, subtraction, or multiplication, as A173419 states on the related OEIS page. In a comment to the sequence, D. Kamenetsky conjectured that a(p) ≥ a(p -1) for every prime. We show that the conjecture is false through four counterexamples below 5000 that satisfy the condition a(p) < a(p -1). They are exactly 3359, 3623, 4909, and 4943.
ER  -