{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T23:59:57Z","timestamp":1776211197292,"version":"3.50.1"},"reference-count":12,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,7,1]],"date-time":"2020-07-01T00:00:00Z","timestamp":1593561600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,7,1]],"date-time":"2020-07-01T00:00:00Z","timestamp":1593561600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001823","name":"Ministerstvo \u0160kolstv\u00ed, Ml\u00e1de\u017ee a T\u011blov\u00fdchovy","doi-asserted-by":"crossref","award":["LM2015070"],"award-info":[{"award-number":["LM2015070"]}],"id":[{"id":"10.13039\/501100001823","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001823","name":"Ministerstvo \u0160kolstv\u00ed, Ml\u00e1de\u017ee a T\u011blov\u00fdchovy","doi-asserted-by":"publisher","award":["LM2018140"],"award-info":[{"award-number":["LM2018140"]}],"id":[{"id":"10.13039\/501100001823","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"published-print":{"date-parts":[[2021,3]]},"DOI":"10.1007\/s11227-020-03368-x","type":"journal-article","created":{"date-parts":[[2020,7,1]],"date-time":"2020-07-01T10:40:10Z","timestamp":1593600010000},"page":"2681-2688","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Convergence verification of the Collatz problem"],"prefix":"10.1007","volume":"77","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0917-5512","authenticated-orcid":false,"given":"David","family":"Barina","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,7,1]]},"reference":[{"key":"3368_CR1","unstructured":"Hercher C (2018) \u00dcber die L\u00e4nge nicht-trivialer Collatz-Zyklen. Die Wurzel 6 and 7"},{"key":"3368_CR2","unstructured":"Lagarias JC (2003) The $$3x+1$$ problem: an annotated bibliography (1963\u20131999) (sorted by author). arXiv:math\/0309224"},{"key":"3368_CR3","unstructured":"Lagarias JC (2006) The $$3x+1$$ problem: an annotated bibliography, II (2000\u20132009). arXiv:math\/0608208"},{"key":"3368_CR4","unstructured":"Conway JH (1972) Unpredictable iterations. In: Proceedings of the 1972 Number Theory Conference, pp 49\u201352"},{"issue":"1","key":"3368_CR5","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1016\/j.tcs.2007.10.020","volume":"390","author":"LD Mol","year":"2008","unstructured":"Mol LD (2008) Tag systems and Collatz-like functions. Theor Comput Sci 390(1):92\u2013101. https:\/\/doi.org\/10.1016\/j.tcs.2007.10.020","journal-title":"Theor Comput Sci"},{"issue":"1","key":"3368_CR6","doi-asserted-by":"publisher","first-page":"3","DOI":"10.2307\/2322189","volume":"92","author":"JC Lagarias","year":"1985","unstructured":"Lagarias JC (1985) The 3x + 1 problem and its generalizations. Am Math Mon 92(1):3\u201323. https:\/\/doi.org\/10.2307\/2322189","journal-title":"Am Math Mon"},{"issue":"1","key":"3368_CR7","first-page":"69","volume":"7","author":"T Honda","year":"2017","unstructured":"Honda T, Ito Y, Nakano K (2017) GPU-accelerated exhaustive verification of the Collatz conjecture. Int J Netw Comput 7(1):69\u201385","journal-title":"Int J Netw Comput"},{"key":"3368_CR8","first-page":"189","volume-title":"The ultimate challenge: The 3x+1 problem","author":"T Oliveira e Silva","year":"2010","unstructured":"Oliveira e Silva T (2010) Empirical verification of the 3x+1 and related conjectures. In: Lagarias JC (ed) The ultimate challenge: The 3x+1 problem. American Mathematical Society, Providence, pp 189\u2013207"},{"issue":"11","key":"3368_CR9","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/0898-1221(92)90034-F","volume":"24","author":"GT Leavens","year":"1992","unstructured":"Leavens GT, Vermeulen M (1992) 3x+1 search programs. Comput Math Appl 24(11):79\u201399. https:\/\/doi.org\/10.1016\/0898-1221(92)90034-F","journal-title":"Comput Math Appl"},{"key":"3368_CR10","unstructured":"Dunn R (1973) On Ulam\u2019s problem. Tech. rep., University of Colorado at Boulder"},{"issue":"225","key":"3368_CR11","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1090\/S0025-5718-99-01031-5","volume":"68","author":"T Oliveira e Silva","year":"1999","unstructured":"Oliveira e Silva T (1999) Maximum excursion and stopping time record-holders for the $$3x+1$$ problem: computational results. Math Comput 68(225):371\u2013384. https:\/\/doi.org\/10.1090\/S0025-5718-99-01031-5","journal-title":"Math Comput"},{"issue":"1","key":"3368_CR12","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1214\/aoap\/1177005779","volume":"2","author":"JC Lagarias","year":"1992","unstructured":"Lagarias JC, Weiss A (1992) The $$3x + 1$$ problem: two stochastic models. Ann Appl Probab 2(1):229\u2013261. https:\/\/doi.org\/10.1214\/aoap\/1177005779","journal-title":"Ann Appl Probab"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-020-03368-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-020-03368-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-020-03368-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,1]],"date-time":"2021-07-01T01:01:35Z","timestamp":1625101295000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-020-03368-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,1]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["3368"],"URL":"https:\/\/doi.org\/10.1007\/s11227-020-03368-x","relation":{},"ISSN":["0920-8542","1573-0484"],"issn-type":[{"value":"0920-8542","type":"print"},{"value":"1573-0484","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,7,1]]},"assertion":[{"value":"1 July 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}