{"paper":{"title":"On generalized Stanley sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Csaba S\\'andor, Quan-Hui Yang, S\\'andor Z. Kiss","submitted_at":"2017-10-05T09:37:53Z","abstract_excerpt":"Let $\\mathbb{N}$ denote the set of all nonnegative integers. Let $k\\ge 3$ be an integer and $A_{0} = \\{a_{1}, \\dots{}, a_{t}\\}$ $(a_{1} < \\ldots< a_{t})$ be a nonnegative set which does not contain an arithmetic progression of length $k$. We denote $A = \\{a_{1}, a_{2}, \\dots{}\\}$ defined by the following greedy algorithm: if $l \\ge t$ and $a_{1}, \\dots{}, a_{l}$ have already been defined, then $a_{l+1}$ is the smallest integer $a > a_{l}$ such that $\\{a_{1}, \\dots{}, a_{l}\\} \\cup \\{a\\}$ also does not contain a $k$-term arithmetic progression. This sequence $A$ is called the Stanley sequence of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01939","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}