{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:35:39Z","timestamp":1753889739356,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2015,12,14]],"date-time":"2015-12-14T00:00:00Z","timestamp":1450051200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>By introducing the busy beaver competition of Turing machines, in 1962, Rado\ndefined noncomputable functions on positive integers. The study of these\nfunctions and variants leads to many mathematical challenges. This article\ntakes up the following one: How can a small Turing machine manage to produce\nvery big numbers? It provides the following answer: mostly by simulating\nCollatz-like functions, that are generalizations of the famous 3x+1 function.\nThese functions, like the 3x+1 function, lead to new unsolved problems in\nnumber theory.<\/jats:p>","DOI":"10.2168\/lmcs-11(4:10)2015","type":"journal-article","created":{"date-parts":[[2016,11,21]],"date-time":"2016-11-21T13:46:40Z","timestamp":1479736000000},"source":"Crossref","is-referenced-by-count":3,"title":["Problems in number theory from busy beaver competition"],"prefix":"10.46298","volume":"Volume 11, Issue 4","author":[{"given":"Pascal","family":"Michel","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2015,12,14]]},"reference":[{"key":"1148:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/1611\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/1611\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:07:46Z","timestamp":1681243666000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/1611"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,14]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-11(4:10)2015","relation":{"is-same-as":[{"id-type":"arxiv","id":"1311.1029","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1311.1029","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2015,12,14]]},"article-number":"1611"}}