{
  "abstract": "In this paper we explore the world of $t$-sumfree sequences, primarily for $t=2$ and $t=3$. Starting with $t$ increasing positive integers, build an infinite sequence by choosing as the next entry the least positive integer that is not the sum of $t$ distinct previous values. The main open problem concerns the question of the conjectured ultimate periodicity of these sequences. We formulate a sufficient condition to prove that a conjectured preperiod and period are correct. We also prove periodicity for a considerable subclass of 2-sumfree and of 3-sumfree sequences. Finally, we present the results of extensive computations on 3-sumfree sequences.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16843",
  "author_total": 2,
  "authors": [
    {
      "name": "Daan van Berkel"
    },
    {
      "name": "Wieb Bosma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dkg9g29kemxm9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16843",
  "fulltext_url": null,
  "id": "dkg9g29kemxm9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16843",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213401224",
  "pdf_url": "https://arxiv.org/pdf/2609.16843",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dkg9g29kemxm9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16843",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16843"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On $t$-sumfree sequences",
  "title_text": "On t-sumfree sequences",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/dkg9g29kemxm9",
  "venue": "arXiv",
  "versions": []
}