{
  "abstract": "The Yellowstone permutation (OEIS A098550) is defined by a(1), a(2), a(3) = 1, 2, 3 and, for n >= 4, a(n) is the least positive integer not yet used with gcd(a(n), a(n-2)) > 1 and gcd(a(n), a(n-1)) = 1. Applegate, Havermann, Selcoe, Shevelev, Sloane and Zumkeller (2015) proved that it is a permutation of the positive integers; its growth was described only empirically. We prove the near-linear bound a(n) <= n (ln n)^7 for every n >= 3, and a(n) <= n (ln n)^6 for ln n >= 73.5, as well as the elementary form a(n) <= n 2^(4 ln n / ln ln n) for every n >= 3. The method is a fixed-time iteration: the anchor a(n-2) of a large term determines the term, the primes of the anchor are forced to have many used multiples in a short window below the term, and a Bonferroni count shows that such heavy primes are too few to supply all the anchors. The coprimality input is a self-contained explicit form of Brun's sieve. The explicit constants are computer-assisted: the first 10^8 terms, and a finite list of explicit inequalities checked on cells of ln n in [ln 10^8, 10^40]; beyond ln n = 10^40 the proof is by hand. OEIS Conjecture 7, a(n) <= (pi/2) n ln n, remains open. Manuscript; not submitted to a journal. The results were developed with an AI system (Anthropic Claude) and checked by independent AI referee agents; no human peer review has taken place. A continuation, The Yellowstone permutation, II (doi:10.5281/zenodo.23449375), proves the asymptotic bound a(n) <= (e^gamma/2 + o(1)) n ln n lnlnln n by a different method, and reduces OEIS Conjecture 7 for large n to counting hypotheses. The theorems and constants of this manuscript are unchanged.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Tomer Haver"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0sbpctkvdw9g7.bib",
  "cited_by": 5,
  "doi": "10.5281/zenodo.23437782",
  "fulltext_url": null,
  "id": "0sbpctkvdw9g7",
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  "landing_url": "https://doi.org/10.5281/zenodo.23437782",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7222829052",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": "European Organization for Nuclear Research",
  "ris": "https://research.draconitic.com/paper/0sbpctkvdw9g7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:17Z",
      "native_id": "W7222829052",
      "source": "openalex",
      "url": "https://doi.org/10.5281/zenodo.23437782"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2602|Analytic Number Theory Research",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A near-linear upper bound for the Yellowstone permutation: a(n) <= n (ln n)^7 for every n >= 3",
  "title_text": "A near-linear upper bound for the Yellowstone permutation: a(n) <= n (ln n)^7 for every n >= 3",
  "type": "peer-reviewed",
  "updated_at": "2026-11-06T13:20:22Z",
  "url": "https://research.draconitic.com/paper/0sbpctkvdw9g7",
  "venue": "Zenodo (CERN European Organization for Nuclear Research)",
  "versions": []
}