{
  "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) $\\ge$ 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28512",
  "author_total": 1,
  "authors": [
    {
      "name": "Rosario Patanè"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/05yjg7k4g765p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28512",
  "fulltext_url": null,
  "id": "05yjg7k4g765p",
  "issns": [],
  "landing_url": "https://hal.science/hal-05756029v1",
  "language": "en",
  "licence": "LicenseRef-publisher-terms",
  "licence_label": "Publisher terms",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GM"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-co"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
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  "openalex": "W7214139455",
  "pdf_url": "https://hal.science/hal-05756029/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/05yjg7k4g765p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:36Z",
      "native_id": "hal-05756029",
      "source": "hal",
      "url": "https://hal.science/hal-05756029v1"
    },
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.28512",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28512"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-co",
      "subfield": "combinatorics"
    }
  ],
  "title": "Counterexamples to a conjecture of Kamenetsky on OEIS A173419",
  "title_text": "Counterexamples to a conjecture of Kamenetsky on OEIS A173419",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/05yjg7k4g765p",
  "venue": "HAL",
  "versions": []
}