On the mathematical model of the transformation of natural numbers by a function of a split type

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dc.citation.epage50
dc.citation.issue2
dc.citation.journalTitleКомп’ютерні системи проектування. Теорія і практика
dc.citation.spage44
dc.citation.volume6
dc.contributor.affiliationНаціональний університет “Львівська політехніка”
dc.contributor.affiliationНаціональний університет “Львівська політехніка”
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.authorКособуцький, Петро
dc.contributor.authorНестор, Наталія
dc.contributor.authorKosobutskyy, Petro
dc.contributor.authorNestor, Nataliia
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-12-15T08:11:16Z
dc.date.created2024-08-10
dc.date.issued2024-08-10
dc.description.abstractУ роботі обґрунтовано некоректність алгоритму, запропонованого в публікації M. Remer [A Comparative Analysis of the New –3(–n) – 1 Remer Conjecture and a Proof of the 3n + 1 Collatz Conjecture. Journal of Applied Mathematics and Physics, Vol. 11, No. 8, August 2023”] в термінах гіпотези Коллатца, а також те, що перетворення –3(–n) – 1 не еквівалентне гіпотезі Коллатца про натуральні числа 3n + 1. Отримані результати можуть бути використані в подальших дослідженнях.
dc.description.abstractIn this work justified incorrectness of the algorithm proposed in the publication M. Remer [A Comparative Analysis of the New –3(–n) – 1 Remer Conjecture and a Proof of the 3n + 1 Collatz Conjecture. Journal of Applied Mathematics and Physics, Vol. 11, No. 8, August 2023] in terms of the Collatz conjecture. And also that the transformation –3(–n) – 1 is not equivalent to Collatz’s conjecture on the natural numbers 3n + 1. The obtained results can be used in further studies of the Collatz hypothesis.
dc.format.extent44-50
dc.format.pages7
dc.identifier.citationKosobutskyy P. On the mathematical model of the transformation of natural numbers by a function of a split type / Petro Kosobutskyy, Nataliia Nestor // Computer Systems of Design. Theory and Practice. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 6. — No 2. — P. 44–50.
dc.identifier.citation2015Kosobutskyy P., Nestor N. On the mathematical model of the transformation of natural numbers by a function of a split type // Computer Systems of Design. Theory and Practice, Lviv. 2024. Vol 6. No 2. P. 44–50.
dc.identifier.citationenAPAKosobutskyy, P., & Nestor, N. (2024). On the mathematical model of the transformation of natural numbers by a function of a split type. Computer Systems of Design. Theory and Practice, 6(2), 44-50. Lviv Politechnic Publishing House..
dc.identifier.citationenCHICAGOKosobutskyy P., Nestor N. (2024) On the mathematical model of the transformation of natural numbers by a function of a split type. Computer Systems of Design. Theory and Practice (Lviv), vol. 6, no 2, pp. 44-50.
dc.identifier.doihttps://doi.org/10.23939/cds2024.02.044
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/124057
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofКомп’ютерні системи проектування. Теорія і практика, 2 (6), 2024
dc.relation.ispartofComputer Systems of Design. Theory and Practice, 2 (6), 2024
dc.relation.references[1] M. Remer. “A Comparative Analysis of the New –3(–n) – 1 Remer Conjecture and a Proof of the 3n + 1 Collatz Conjecture”, Journal of Applied Mathematics and Physics, Vol. 11, No. 8, August 2023, https://doi.org/10.4236/jamp.2023.118143
dc.relation.references[2] J. Lagarias. “The 3x + 1 problem: An annotated bibliography II (2000–2009)”, 2012, arXiv:math/0608208.
dc.relation.references[3] A. Grubiy. “Automaton implementations of the process of generating a Collatz sequence”, Cybernetics and Systems Analysis, 48, No. 1, 108–116 (2012), https://doi.org/10.1007/s10559-012-9380-4
dc.relation.references[4] I. Rystsov, “Some remarks about the Collatz problem”, Cybernetics and Systems Analysis, 49, No. 3, 353–365 (2013), https://doi.org/10.1007/s10559-013-9518-z
dc.relation.references[5] D. Xu, D. Tamir, “Pseudo-random number generators based on the Collatz Conjecture”, Int. j. inf. tecnol. (2019) 11:453–459, https://doi.org/10.1007/s41870-019-00307-9
dc.relation.references[6] P. Kosobutskyy, “The Collatz problem as a reverse problem on a graph tree formed from Q×2^n (Q = 1,3,5,7,…) Jacobsthal-type numbers” .arXiv:2306.14635v1
dc.relation.references[7] Р. Kosobutsky, “Svitohliad 2022, No. 5 (97), 56–61(Ukraine). ISSN 2786-6882 (Online); ISSN 1819-7329.
dc.relation.references[8] Р. Kosobutskyy, Comment from article “M. Ahmed, Two different scenarios when the Collatz Conjecture fails. General Letters in Mathematics. 2023”, https://www.refaad.com/Journal/Article/1388,https://doi.org/10.31559/glm2022.12.4.4
dc.relation.references[9] P. Kosobutskyy, A. Yedyharova, T. Slobodzyan. From Newtons binomial and Pascal’striangle to Collatz problem.CDS.2023; Vol. 5, No. 1: 121–127, https://doi.org/10.23939/cds2023.01.121
dc.relation.references[10] P. Kosobutskyy, D. Rebot. Collatz Conjecture 3n±1 as a Newton Binomial Problem. CDS. 2023; Vol. 5, No. 1: 137–145, https://doi.org/10.23939/cds2023.01.137
dc.relation.references[11] A. Horadam. 1996. Jacobsthal Representation Numbers. Fibonacci Quarterly. 34, 40–54
dc.relation.references[12] M. Stein, S. Ulam; M. Well. (1964). American Mathematical Monthly, 71(5):516–520; M.Stein, S.Ulam. (1967) American Mathematical Monthly, 74(1) : 43–44, https://doi.org/10.2307/2314055
dc.relation.references[13] P. Kosobutsky. Lviv mathematician Stanislav Ulam is the creator of the statistical modeling method or the Monte Carlo method. The world of physics. 2012, No. 4, 22–30.
dc.relation.references[14] L. Green. The Negative Collatz Sequence. (2022), v1.25.
dc.relation.references[15] N. Sloane. The On-line encyclopedia of integer sequences. The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Available online. https://oeis.org/A002450
dc.relation.referencesen[1] M. Remer. "A Comparative Analysis of the New –3(–n) – 1 Remer Conjecture and a Proof of the 3n + 1 Collatz Conjecture", Journal of Applied Mathematics and Physics, Vol. 11, No. 8, August 2023, https://doi.org/10.4236/jamp.2023.118143
dc.relation.referencesen[2] J. Lagarias. "The 3x + 1 problem: An annotated bibliography II (2000–2009)", 2012, arXiv:math/0608208.
dc.relation.referencesen[3] A. Grubiy. "Automaton implementations of the process of generating a Collatz sequence", Cybernetics and Systems Analysis, 48, No. 1, 108–116 (2012), https://doi.org/10.1007/s10559-012-9380-4
dc.relation.referencesen[4] I. Rystsov, "Some remarks about the Collatz problem", Cybernetics and Systems Analysis, 49, No. 3, 353–365 (2013), https://doi.org/10.1007/s10559-013-9518-z
dc.relation.referencesen[5] D. Xu, D. Tamir, "Pseudo-random number generators based on the Collatz Conjecture", Int. j. inf. tecnol. (2019) 11:453–459, https://doi.org/10.1007/s41870-019-00307-9
dc.relation.referencesen[6] P. Kosobutskyy, "The Collatz problem as a reverse problem on a graph tree formed from Q×2^n (Q = 1,3,5,7,…) Jacobsthal-type numbers" .arXiv:2306.14635v1
dc.relation.referencesen[7] R. Kosobutsky, "Svitohliad 2022, No. 5 (97), 56–61(Ukraine). ISSN 2786-6882 (Online); ISSN 1819-7329.
dc.relation.referencesen[8] R. Kosobutskyy, Comment from article "M. Ahmed, Two different scenarios when the Collatz Conjecture fails. General Letters in Mathematics. 2023", https://www.refaad.com/Journal/Article/1388,https://doi.org/10.31559/glm2022.12.4.4
dc.relation.referencesen[9] P. Kosobutskyy, A. Yedyharova, T. Slobodzyan. From Newtons binomial and Pascal’striangle to Collatz problem.CDS.2023; Vol. 5, No. 1: 121–127, https://doi.org/10.23939/cds2023.01.121
dc.relation.referencesen[10] P. Kosobutskyy, D. Rebot. Collatz Conjecture 3n±1 as a Newton Binomial Problem. CDS. 2023; Vol. 5, No. 1: 137–145, https://doi.org/10.23939/cds2023.01.137
dc.relation.referencesen[11] A. Horadam. 1996. Jacobsthal Representation Numbers. Fibonacci Quarterly. 34, 40–54
dc.relation.referencesen[12] M. Stein, S. Ulam; M. Well. (1964). American Mathematical Monthly, 71(5):516–520; M.Stein, S.Ulam. (1967) American Mathematical Monthly, 74(1) : 43–44, https://doi.org/10.2307/2314055
dc.relation.referencesen[13] P. Kosobutsky. Lviv mathematician Stanislav Ulam is the creator of the statistical modeling method or the Monte Carlo method. The world of physics. 2012, No. 4, 22–30.
dc.relation.referencesen[14] L. Green. The Negative Collatz Sequence. (2022), v1.25.
dc.relation.referencesen[15] N. Sloane. The On-line encyclopedia of integer sequences. The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Available online. https://oeis.org/A002450
dc.relation.urihttps://doi.org/10.4236/jamp.2023.118143
dc.relation.urihttps://doi.org/10.1007/s10559-012-9380-4
dc.relation.urihttps://doi.org/10.1007/s10559-013-9518-z
dc.relation.urihttps://doi.org/10.1007/s41870-019-00307-9
dc.relation.urihttps://www.refaad.com/Journal/Article/1388,https://doi.org/10.31559/glm2022.12.4.4
dc.relation.urihttps://doi.org/10.23939/cds2023.01.121
dc.relation.urihttps://doi.org/10.23939/cds2023.01.137
dc.relation.urihttps://doi.org/10.2307/2314055
dc.relation.urihttps://oeis.org/A002450
dc.rights.holder© Національний університет „Львівська політехніка“, 2024
dc.rights.holder© Kosobutskyy P., Nestor N., 2024
dc.subjectрекурентна послідовність
dc.subjectчисла Якобсталя
dc.subjectгіпотеза Коллатца
dc.subjectнатуральні числа
dc.subjectгіпотеза
dc.subjectRecurrence sequence
dc.subjectJacobsthal numbers
dc.subjectCollatz conjecture
dc.subjectnatural numbers
dc.subjectconjecture
dc.titleOn the mathematical model of the transformation of natural numbers by a function of a split type
dc.title.alternativeПро математичну модель перетворення натуральних чисел функцією розділеного типу
dc.typeArticle

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Комп'ютерні системи проектування теорія і практика. – 2024. – Том 6, № 2