Recurrence and structuring of sequences of transformations 3n + 1 as arguments for confirmation of the collatz hypothesis

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dc.citation.epage33
dc.citation.issue1
dc.citation.journalTitleКомп’ютерні системи проектування. Теорія і практика.
dc.citation.spage28
dc.citation.volume5
dc.contributor.affiliationНаціональний університет “Львівська політехніка”
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.authorКособуцький, Петро
dc.contributor.authorКаркульовський, Володимир
dc.contributor.authorKosobutskyy, Petro
dc.contributor.authorKarkulovskyy, Volodymyr
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-07-23T06:35:29Z
dc.date.created2023-02-28
dc.date.issued2023-02-28
dc.description.abstractПоказано, що необмеженість підпослідовності непарних чисел не контраргумент порушення гіпотези Коллатца, а універсальна характеристика перетворень натуральних чисел за алгоритмом 3n+1. Встановлений рекурентний зв’язок між параметрами послідовності Коллатца перетворень довільної пари натуральних чисел n і 2n .
dc.description.abstractIt is shown that infinites of the subsequence of odd numbers is not a counterargument of the violation of the Collatz hypothesis, but a universal characteristic of transformations of natural numbers by the 3n + 1 algorithm. A recurrent relationship is established between the parameters of the sequence of Collatz transformations of an arbitrary pair of natural numbers n and 2n.
dc.format.extent28-33
dc.format.pages6
dc.identifier.citationKosobutskyy P. Recurrence and structuring of sequences of transformations 3n + 1 as arguments for confirmation of the collatz hypothesis / Petro Kosobutskyy, Volodymyr Karkulovskyy // Computer Design Systems. Theory and Practice. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 5. — No 1. — P. 28–33.
dc.identifier.citationenKosobutskyy P. Recurrence and structuring of sequences of transformations 3n + 1 as arguments for confirmation of the collatz hypothesis / Petro Kosobutskyy, Volodymyr Karkulovskyy // Computer Design Systems. Theory and Practice. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 5. — No 1. — P. 28–33.
dc.identifier.doidoi.org/10.23939/cds2023.01.028
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/111492
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofКомп’ютерні системи проектування. Теорія і практика., 1 (5), 2023
dc.relation.ispartofComputer Design Systems. Theory and Practice, 1 (5), 2023
dc.relation.references1.L. Collatz On the motivation and origin of the (3n + 1) – Problem, J. Qufu Normal University, Natural Science Edition,1986, 12(3), 9–11.
dc.relation.references2. The On-line encyclopedia of integer sequences. The OEIS Foundation is supported by donations from users Recurrence and Structuring of Sequences of Transformations 3n+1 as Arguments… 33 of the OEIS and by a grant from the Simons Foundation, https://oeis.org/A002450
dc.relation.references3. R. Terras. A stopping time problem on the positive integers. Acta Arith. 1976, 30, 241–252. https://doi.org/10.4064/aa-30-3-241-252
dc.relation.references4. Terras, R. On the Existence of a Density. Acta Arith. 1979, 35, 101–102. https://doi.org/10.4064/aa-35-1-101-102
dc.relation.references5. T. Tao. Almost all orbits of the Collatz map attain almost bounded values, 2020.
dc.relation.references6. A. Rahn, E. Sultanow, M. Henkel, S. Ghosh, I. Aberkane. An Algorithm for Linearizing the Collatz Convergence.Mathematics 2021, 9(16), 1898; https://doi.org/10.3390/math9161898
dc.relation.references7. Collatz conjucture. Collatz best results, https://www.dcode.fr/collatz-conjecture
dc.relation.references8. J. Kleinnijenhuis, A. Kleinnijenhuis, M. Aydogan. The Collatz tree as a Hilbert hotel: a proof of the 3x + 1 conjecture/arXiv:2008.13643v3 [math.GM] 17 Jan 2021
dc.relation.references9. М. Ahmed Maya. Two different scenarios when the Collatz Conjecture fails, arXiv:2001.04976v1 [math.GM]
dc.relation.references10. L. Green. LOG book, http://lesliegreen.byethost3.com/publications.html
dc.relation.references11. Collatz Conjucture, https://www.dcode.fr/collatz-conjecture.
dc.relation.references12. C.Сadogan C. A Solution to the 3x + 1 Problem Charles Cadogan.юCaribb. J. Math. Comput. Sci. — 2006. — 13, p. 1-11
dc.relation.references13. И.Рысцов. Замечание по поводу доказательства гипотезы Коллатца. Украинский математический конгресс – 2009. (UKRAINIAN MATHEMATICAL CONGRESS − 2009 (Dedicated to the Centennial of Nikolai N. Bogoliubov), Kyiv, Institute of Mathematics of NASU, August 27−29, 2009). https://www.imath.kiev.ua/~congress2009/Abstracts/Rystcov.pdf
dc.relation.references14. P.Catarino, H.Campos, P.Vasco. On the Mersenne sequence. Annales Mathematicae et Informaticae, vol.46 (2016), 37-53.
dc.relation.referencesen1.L. Collatz On the motivation and origin of the (3n + 1) – Problem, J. Qufu Normal University, Natural Science Edition,1986, 12(3), 9–11.
dc.relation.referencesen2. The On-line encyclopedia of integer sequences. The OEIS Foundation is supported by donations from users Recurrence and Structuring of Sequences of Transformations 3n+1 as Arguments… 33 of the OEIS and by a grant from the Simons Foundation, https://oeis.org/A002450
dc.relation.referencesen3. R. Terras. A stopping time problem on the positive integers. Acta Arith. 1976, 30, 241–252. https://doi.org/10.4064/aa-30-3-241-252
dc.relation.referencesen4. Terras, R. On the Existence of a Density. Acta Arith. 1979, 35, 101–102. https://doi.org/10.4064/aa-35-1-101-102
dc.relation.referencesen5. T. Tao. Almost all orbits of the Collatz map attain almost bounded values, 2020.
dc.relation.referencesen6. A. Rahn, E. Sultanow, M. Henkel, S. Ghosh, I. Aberkane. An Algorithm for Linearizing the Collatz Convergence.Mathematics 2021, 9(16), 1898; https://doi.org/10.3390/math9161898
dc.relation.referencesen7. Collatz conjucture. Collatz best results, https://www.dcode.fr/collatz-conjecture
dc.relation.referencesen8. J. Kleinnijenhuis, A. Kleinnijenhuis, M. Aydogan. The Collatz tree as a Hilbert hotel: a proof of the 3x + 1 conjecture/arXiv:2008.13643v3 [math.GM] 17 Jan 2021
dc.relation.referencesen9. M. Ahmed Maya. Two different scenarios when the Collatz Conjecture fails, arXiv:2001.04976v1 [math.GM]
dc.relation.referencesen10. L. Green. LOG book, http://lesliegreen.byethost3.com/publications.html
dc.relation.referencesen11. Collatz Conjucture, https://www.dcode.fr/collatz-conjecture.
dc.relation.referencesen12. C.Sadogan C. A Solution to the 3x + 1 Problem Charles Cadogan.iuCaribb. J. Math. Comput. Sci, 2006, 13, p. 1-11
dc.relation.referencesen13. I.Rystsov. Zamechanie po povodu dokazatelstva hipotezy Kollattsa. Ukrainskii matematicheskii konhress – 2009. (UKRAINIAN MATHEMATICAL CONGRESS − 2009 (Dedicated to the Centennial of Nikolai N. Bogoliubov), Kyiv, Institute of Mathematics of NASU, August 27−29, 2009). https://www.imath.kiev.ua/~congress2009/Abstracts/Rystcov.pdf
dc.relation.referencesen14. P.Catarino, H.Campos, P.Vasco. On the Mersenne sequence. Annales Mathematicae et Informaticae, vol.46 (2016), 37-53.
dc.relation.urihttps://oeis.org/A002450
dc.relation.urihttps://doi.org/10.4064/aa-30-3-241-252
dc.relation.urihttps://doi.org/10.4064/aa-35-1-101-102
dc.relation.urihttps://doi.org/10.3390/math9161898
dc.relation.urihttps://www.dcode.fr/collatz-conjecture
dc.relation.urihttp://lesliegreen.byethost3.com/publications.html
dc.relation.urihttps://www.imath.kiev.ua/~congress2009/Abstracts/Rystcov.pdf
dc.rights.holder© Національний університет “Львівська політехніка”, 2023
dc.rights.holder© Kособуцький П., Kаркульовський В., 2023
dc.subjectгіпотеза Коллатца
dc.subjectпослідовність
dc.subjectперетворення 3n+1
dc.subjectнатуральні числа
dc.subjectCollatz conjecture
dc.subjectrecurrent sequence
dc.subjecttransformation 3n + 1
dc.subjectnatural numbers
dc.titleRecurrence and structuring of sequences of transformations 3n + 1 as arguments for confirmation of the collatz hypothesis
dc.title.alternativeЗакономірності формування послідовностей 3n+1 перетворень як аргумент підтвердження гіпотези Коллатца
dc.typeArticle

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Комп'ютерні системи проектування теорія і практика. – 2023. – Том 5, № 1