{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T08:20:52Z","timestamp":1761294052617,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A subsequence of the sequence $(1,2,...,n)$ is called a 3-$AP$-free sequence if it does not contain any three term arithmetic progression. By $r(n)$ we denote the length of the longest such 3-$AP$-free sequence. The exact values of the function $r(n)$ were known, for $n\\leq 27$ and $41\\leq n \\leq 43$. In the present paper we determine, with a use of computer, the exact values, for all $n\\leq 123$. The value $r(122)=32$ shows that the Szekeres' conjecture holds for $k=5$.<\/jats:p>","DOI":"10.37236\/2061","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:29:15Z","timestamp":1578695355000},"source":"Crossref","is-referenced-by-count":4,"title":["Sequences Containing No 3-Term Arithmetic Progressions"],"prefix":"10.37236","volume":"19","author":[{"given":"Janusz","family":"Dybizba\u0144ski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2012,4,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i2p15\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i2p15\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T17:36:15Z","timestamp":1579282575000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i2p15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,4,27]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2012,4,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2061","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,4,27]]},"article-number":"P15"}}