Efficient Computation of Collatz Sequence Stopping Times: A Novel Algorithmic Approach

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, achiev...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:IEEE access Ročník 13; s. 41210 - 41220
Hlavní autori: Getachew, Eyob Solomon, Assefa, Beakal Gizachew
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: IEEE 2025
Predmet:
Algorithm optimization
and large-scale verification
Approximation algorithms
bitwise operations
Collatz conjecture
Collatz tree
Complexity theory
computational complexity
Computational efficiency
computational mathematics
Encryption
high-performance algorithms
logarithmic complexity
memoization
Optimization
parallel computing
Probabilistic logic
sequence analysis
stopping time
Testing
Time complexity
Visualization
Watermarking
ISSN:2169-3536, 2169-3536
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
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.
AbstractList 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.
Author Getachew, Eyob Solomon
Assefa, Beakal Gizachew
Author_xml – sequence: 1
  givenname: Eyob Solomon
  orcidid: 0009-0009-5766-2041
  surname: Getachew
  fullname: Getachew, Eyob Solomon
  email: eyob.solomon@aait.edu.et
  organization: School of Information Technology and Engineering, Addis Ababa Institute of Technology, Addis Ababa, Ethiopia
– sequence: 2
  givenname: Beakal Gizachew
  orcidid: 0000-0001-9510-5216
  surname: Assefa
  fullname: Assefa, Beakal Gizachew
  organization: School of Information Technology and Engineering, Addis Ababa Institute of Technology, Addis Ababa, Ethiopia
BookMark eNp9kF1PwyAUhonRxK_9Ar3gD2xCKW3xrmmmLln0YuotoXCYmK5Uykz019tZTRYv5OZw3uR5A88pOmx9CwhdUDKjlIirsqrmq9UsIQmfMZ4WhNEDdJLQTEwZZ9nh3v0YTfr-lQynGCKen6DnubVOO2gjrvym20YVnW-xt8PaNCp-4hW8baHVgFfRd51r1_jRbaC_xiW-9-_Q4LJZ--Diy8ZpXHZd8Eq_nKMjq5oeJj_zDD3dzB-ru-ny4XZRlcupZgWLU5ULS3IQha2NhiwXQgliKLUFsYakkNg0NXVBqKDaMAqcG6MzqMkQ0zpJ2BlajL3Gq1fZBbdR4UN65eR34MNaqhCdbkByU0PGM2FILVIrhu9bJWjKU2YLELkeusTYpYPv-wBWajfqiEG5RlIid77l6FvufMsf3wPL_rC_b_mfuhwpBwB7hKCEFpx9Afn5jqs
CODEN IAECCG
CitedBy_id crossref_primary_10_1080_27684830_2025_2542052
crossref_primary_10_3390_info16090745
Cites_doi 10.3390/e20120901
10.1109/SmartWorld.2018.00099
10.1080/01611194.2020.1821408
10.5937/vojtehg72-50306
10.1016/j.dib.2019.104537
10.1016/j.chaos.2023.114103
10.1016/j.jisa.2019.02.010
10.5642/jhummath.YQHO7207
10.1155/2021/5754439
10.1109/HPCC/SmartCity/DSS.2019.00382
10.1109/cais.2019.8769514
10.1109/ACCESS.2024.3349470
10.59287/as-ijanser.637
10.1016/j.bspc.2021.102936
10.33140/JCTCSR.03.03.07
ContentType Journal Article
DBID 97E
ESBDL
RIA
RIE
AAYXX
CITATION
DOA
DOI 10.1109/ACCESS.2025.3548031
DatabaseName IEEE Xplore (IEEE)
IEEE Xplore Open Access Journals
IEEE All-Society Periodicals Package (ASPP) 1998–Present
IEEE Electronic Library (IEL)
CrossRef
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
DatabaseTitleList

Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
– sequence: 2
  dbid: RIE
  name: IEEE Electronic Library (IEL)
  url: https://ieeexplore.ieee.org/
  sourceTypes: Publisher
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 2169-3536
EndPage 41220
ExternalDocumentID oai_doaj_org_article_5dbe6569d0b94f9695fa914543f8e97c
10_1109_ACCESS_2025_3548031
10910185
Genre orig-research
GroupedDBID 0R~
4.4
5VS
6IK
97E
AAJGR
ABAZT
ABVLG
ACGFS
ADBBV
AGSQL
ALMA_UNASSIGNED_HOLDINGS
BCNDV
BEFXN
BFFAM
BGNUA
BKEBE
BPEOZ
EBS
EJD
ESBDL
GROUPED_DOAJ
IPLJI
JAVBF
KQ8
M43
M~E
O9-
OCL
OK1
RIA
RIE
RNS
AAYXX
CITATION
ID FETCH-LOGICAL-c383t-a79f07e98fbdce6799a90d11f80fd04e2f44db80191cd31e55ddc6eb044d1b223
IEDL.DBID RIE
ISICitedReferencesCount 2
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001442938700011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 2169-3536
IngestDate Fri Oct 03 12:41:48 EDT 2025
Tue Nov 18 19:52:49 EST 2025
Sat Nov 29 08:11:43 EST 2025
Wed Aug 27 01:47:40 EDT 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Language English
License https://creativecommons.org/licenses/by/4.0/legalcode
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c383t-a79f07e98fbdce6799a90d11f80fd04e2f44db80191cd31e55ddc6eb044d1b223
ORCID 0000-0001-9510-5216
0009-0009-5766-2041
OpenAccessLink https://ieeexplore.ieee.org/document/10910185
PageCount 11
ParticipantIDs crossref_citationtrail_10_1109_ACCESS_2025_3548031
ieee_primary_10910185
doaj_primary_oai_doaj_org_article_5dbe6569d0b94f9695fa914543f8e97c
crossref_primary_10_1109_ACCESS_2025_3548031
PublicationCentury 2000
PublicationDate 20250000
2025-00-00
2025-01-01
PublicationDateYYYYMMDD 2025-01-01
PublicationDate_xml – year: 2025
  text: 20250000
PublicationDecade 2020
PublicationTitle IEEE access
PublicationTitleAbbrev Access
PublicationYear 2025
Publisher IEEE
Publisher_xml – name: IEEE
References Abascal (ref4) 2024
ref13
ref12
Boulkaboul (ref7) 2022
ref15
Ebnenasir (ref6) 2024
ref14
ref20
ref11
ref10
ref2
ref1
Venkatesulu (ref3) 2020; 2
ref17
ref16
ref19
ref18
Inselmann (ref5) 2024
ref8
ref9
(ref21) 2024
References_xml – ident: ref19
  doi: 10.3390/e20120901
– year: 2024
  ident: ref4
  article-title: Bottom-up approach to the collatz conjecture
  publication-title: Authorea Preprints
– year: 2024
  ident: ref6
  article-title: Specifying and verifying the convergence stairs of the collatz program
  publication-title: arXiv:2403.04777
– ident: ref2
  doi: 10.1109/SmartWorld.2018.00099
– year: 2022
  ident: ref7
  article-title: 3n + 3k: New perspective on collatz conjecture
  publication-title: arXiv:2212.00073
– ident: ref18
  doi: 10.1080/01611194.2020.1821408
– ident: ref9
  doi: 10.5937/vojtehg72-50306
– ident: ref15
  doi: 10.1016/j.dib.2019.104537
– ident: ref17
  doi: 10.1016/j.chaos.2023.114103
– ident: ref14
  doi: 10.1016/j.jisa.2019.02.010
– ident: ref8
  doi: 10.5642/jhummath.YQHO7207
– ident: ref11
  doi: 10.1155/2021/5754439
– ident: ref12
  doi: 10.1109/HPCC/SmartCity/DSS.2019.00382
– ident: ref13
  doi: 10.1109/cais.2019.8769514
– ident: ref16
  doi: 10.1109/ACCESS.2024.3349470
– year: 2024
  ident: ref5
  article-title: An approximation of the collatz map and a lower bound for the average total stopping time
  publication-title: arXiv:2402.03276
– volume: 2
  start-page: 71
  year: 2020
  ident: ref3
  article-title: Verification of collatz conjecture: An algorithmic approach
  publication-title: WSEAS Trans. Eng. World
– ident: ref1
  doi: 10.59287/as-ijanser.637
– ident: ref20
  doi: 10.1016/j.bspc.2021.102936
– ident: ref10
  doi: 10.33140/JCTCSR.03.03.07
– volume-title: ChatGPT: Language Model for Text Generation and Assistance
  year: 2024
  ident: ref21
SSID ssj0000816957
Score 2.3477721
Snippet The Collatz conjecture, which posits that any positive integer will eventually reach 1 through a specific iterative process, is a classic unsolved problem in...
SourceID doaj
crossref
ieee
SourceType Open Website
Enrichment Source
Index Database
Publisher
StartPage 41210
SubjectTerms Algorithm optimization
and large-scale verification
Approximation algorithms
bitwise operations
Collatz conjecture
Collatz tree
Complexity theory
computational complexity
Computational efficiency
computational mathematics
Encryption
high-performance algorithms
logarithmic complexity
memoization
Optimization
parallel computing
Probabilistic logic
sequence analysis
stopping time
Testing
Time complexity
Visualization
Watermarking
SummonAdditionalLinks – databaseName: DOAJ Directory of Open Access Journals
  dbid: DOA
  link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrZ07T8MwEMcthBhgQDxFeckDIwE7cWIfW6mKmCqkAuoW-VkqQYNK6MCnx3ZC1S6wsFqO4_xz8t1Z9u8Quii41LlmPJGMyoTJcFnZZVlSOOPDBSVUakksNsEHAzEawcNSqa9wJqzBAzfCXedGWR9zgCEKmIMCcieBspxlTljgOqy-hMNSMhXXYEF9T95ihiiB626v57_IJ4RpfpUFyFlGV1xRJPavlFiJHuZuB223oSHuNlPaRWt2uoe2loCB--i5H4kP3lHgphxD1BVXDocNAFl_4WF7NBoP6yqgF8Y4XvK4wV08qObWD_86rmaT-uVtonG3BYofoKe7_mPvPmkrIyTaZ5R1Ijk4wi0Ip4y2BQfwIhtKnSDOEGZTx5hR3vkA1SajNs-N0YVVxDdT5SOCQ7Q-rab2CGEuMuM1ESorBANrgMkipS41hutCctdB6Y9IpW6x4aF6xWsZ0wcCZaNsGZQtW2U76HLx0HtDzfi9-21Qf9E1IK9jgzeEsjWE8i9D6KCD8O-W3geBRpYf_8fgJ2gzTLjZezlF6_Xs056hDT2vJx-z82h734Cf2ns
  priority: 102
  providerName: Directory of Open Access Journals
Title Efficient Computation of Collatz Sequence Stopping Times: A Novel Algorithmic Approach
URI https://ieeexplore.ieee.org/document/10910185
https://doaj.org/article/5dbe6569d0b94f9695fa914543f8e97c
Volume 13
WOSCitedRecordID wos001442938700011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAON
  databaseName: DOAJ Directory of Open Access Journals
  customDbUrl:
  eissn: 2169-3536
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000816957
  issn: 2169-3536
  databaseCode: DOA
  dateStart: 20130101
  isFulltext: true
  titleUrlDefault: https://www.doaj.org/
  providerName: Directory of Open Access Journals
– providerCode: PRVHPJ
  databaseName: ROAD: Directory of Open Access Scholarly Resources
  customDbUrl:
  eissn: 2169-3536
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000816957
  issn: 2169-3536
  databaseCode: M~E
  dateStart: 20130101
  isFulltext: true
  titleUrlDefault: https://road.issn.org
  providerName: ISSN International Centre
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3NT9swFLeg4rAdYGydVmDIhx0XGidOHHMrVREXKiS2iVvkj2dWqTRTSXvgwN_Os2MqOAyJSxRZz4njn6P3Yb_fI-RHKZQpDBeJ4kwlXPlkZZfnSeksmgu60hmkodiEmE6rmxt5FZPVQy4MAITDZ3Dib8Nevm3MyofKhp7EMkUFs022hSi7ZK1NQMVXkJCFiMxCKDocjcf4EegDZsVJ7nnNcvZK-wSS_ldVVYJSOd9753A-kd1oPdJRB_c-2YLFZ_LxBafgF_JnEkghsCftKjaEqaeNoz5GoNoHeh1PT9PrtvHsDLc05IGc0hGdNmvAx89vm-Ws_Xs3M3QUOcf75Pf55Nf4IonFExKDTmebKCFdKkBWTlsDpZAScbCMuSp1NuWQOc6tRv0kmbE5g6Kw1pSgU2xmGo2Gr6S3aBbwjVBR5RbnsNJ5WXEJVnJVZsxl1gpTKuEGJHue1NpEZnFf4GJeBw8jlXWHRO2RqCMSA_Jz0-lfR6zxtviZR2sj6lmxQwMiUsefrC6sBrRPpU215E7icnBKMl7w3FUghRmQvkfxxfs6AA_-035IPvgxdBGXI9Jrlyv4TnbMup3dL4-D-47Xy8fJcViKT_A-2jE
linkProvider IEEE
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1NT9wwEB3BUolygJZSdSm0PvTYgJ04ccxtu2JFVbqqBEXcIn-MYSW6qbaBA78e23FXcGglbtFonDjzHM144nkD8KkSypSGi0xxpjKuQrGyK4qsctaHC7rWOdLYbEJMp_XlpfyRitVjLQwixsNneBAu479825rbkCo7DCSW1DuYVVgrOc9pX661TKmEHhKyFIlbyCsfjsZj_xp-F5iXB0VgNivYE_8Tafqf9FWJbmWy9cwJvYLNFD-SUQ_4a1jB-TZsPGIVfAMXx5EWwo8kfc-GaHzSOhKyBKq7J2fp_DQ569rAz3BFYiXIERmRaXuH_vY3V-1i1l3_mhkySqzjO_Bzcnw-PslS-4TM-G1nlykhHRUoa6etwUpI6ZGwjLmaOks55o5zq72HkszYgmFZWmsq1NSLmfZhw1sYzNs5vgMi6sJ6G9a6qGou0Uquqpy53FphKiXcEPK_Rm1M4hYPLS5umrjHoLLpkWgCEk1CYgifl4N-99Qa_1f_EtBaqgZe7CjwiDTpM2tKq9FHqNJSLbmTfjk4JRkveeFqlMIMYSeg-Oh5PYC7_5B_hPWT8--nzenX6bf38DLMp8-_7MGgW9ziPrwwd93sz-JDXIoPJzrbUg
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Efficient+Computation+of+Collatz+Sequence+Stopping+Times%3A+A+Novel+Algorithmic+Approach&rft.jtitle=IEEE+access&rft.au=Getachew%2C+Eyob+Solomon&rft.au=Assefa%2C+Beakal+Gizachew&rft.date=2025&rft.pub=IEEE&rft.eissn=2169-3536&rft.volume=13&rft.spage=41210&rft.epage=41220&rft_id=info:doi/10.1109%2FACCESS.2025.3548031&rft.externalDocID=10910185
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2169-3536&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2169-3536&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2169-3536&client=summon