{"title":"Efficient Computation of Collatz Sequence Stopping Times: A Novel Algorithmic Approach","authors":"Eyob Solomon Getachew;Beakal Gizachew Assefa","doi":"10.1109/ACCESS.2025.3548031","DOIUrl":null,"url":null,"abstract":"The Collatz conjecture, which posits that any positive integer will eventually reach 1 through a specific iterative process, is a classic unsolved problem in mathematics. This research focuses on designing an efficient algorithm to compute the stopping time of numbers in the Collatz sequence, achieving significant computational improvements. By leveraging structural patterns in the Collatz tree, the proposed algorithm minimizes redundant operations and optimizes computational steps. Unlike prior methods, it efficiently handles extremely large numbers without requiring advanced techniques such as memoization or parallelization. Experimental evaluations confirm computational efficiency improvements of approximately 28% over state-of-the-art methods. These findings underscore the algorithm’s scalability and robustness, providing a foundation for future large-scale verification of the conjecture and potential applications in computational mathematics.","PeriodicalId":13079,"journal":{"name":"IEEE Access","volume":"13 ","pages":"41210-41220"},"PeriodicalIF":3.4000,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10910185","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Access","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10910185/","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
The Collatz conjecture, which posits that any positive integer will eventually reach 1 through a specific iterative process, is a classic unsolved problem in mathematics. This research focuses on designing an efficient algorithm to compute the stopping time of numbers in the Collatz sequence, achieving significant computational improvements. By leveraging structural patterns in the Collatz tree, the proposed algorithm minimizes redundant operations and optimizes computational steps. Unlike prior methods, it efficiently handles extremely large numbers without requiring advanced techniques such as memoization or parallelization. Experimental evaluations confirm computational efficiency improvements of approximately 28% over state-of-the-art methods. These findings underscore the algorithm’s scalability and robustness, providing a foundation for future large-scale verification of the conjecture and potential applications in computational mathematics.
IEEE AccessCOMPUTER SCIENCE, INFORMATION SYSTEMSENGIN-ENGINEERING, ELECTRICAL & ELECTRONIC
CiteScore
9.80
自引率
7.70%
发文量
6673
审稿时长
6 weeks
期刊介绍:
IEEE Access® is a multidisciplinary, open access (OA), applications-oriented, all-electronic archival journal that continuously presents the results of original research or development across all of IEEE''s fields of interest.
IEEE Access will publish articles that are of high interest to readers, original, technically correct, and clearly presented. Supported by author publication charges (APC), its hallmarks are a rapid peer review and publication process with open access to all readers. Unlike IEEE''s traditional Transactions or Journals, reviews are "binary", in that reviewers will either Accept or Reject an article in the form it is submitted in order to achieve rapid turnaround. Especially encouraged are submissions on:
Multidisciplinary topics, or applications-oriented articles and negative results that do not fit within the scope of IEEE''s traditional journals.
Practical articles discussing new experiments or measurement techniques, interesting solutions to engineering.
Development of new or improved fabrication or manufacturing techniques.
Reviews or survey articles of new or evolving fields oriented to assist others in understanding the new area.