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Relevant bibliographies by topics / Conjecture de Collatz

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Academic literature on the topic 'Conjecture de Collatz'

Author: Grafiati

Published: 4 June 2021

Last updated: 17 February 2022

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Journal articles on the topic "Conjecture de Collatz"

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Gutierrez, Amauri. "Collatz conjecture revisited: an elementary generalization." Acta Universitatis Sapientiae, Mathematica 12, no. 1 (2020): 112–27. http://dx.doi.org/10.2478/ausm-2020-0007.

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AbstractCollatz conjecture states that iterating the map that takes even natural number n to {n \over 2} and odd natural number n to 3n + 1, will eventually obtain 1. In this paper a new generalization of the Collatz conjecture is analyzed and some interesting results are obtained. Since Collatz conjecture can be seen as a particular case of the generalization introduced in this articule, several more general conjectures are also presented.

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Hebda, Sebastian. "On the Collatz conjecture." Colloquium Mathematicum 133, no. 2 (2013): 189–95. http://dx.doi.org/10.4064/cm133-2-5.

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邹, 山中. "Proof of Collatz Conjecture." Pure Mathematics 09, no. 03 (2019): 414–16. http://dx.doi.org/10.12677/pm.2019.93055.

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4

Andrei, Ştefan, and Cristian Masalagiu. "About the Collatz conjecture." Acta Informatica 35, no. 2 (1998): 167–79. http://dx.doi.org/10.1007/s002360050117.

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Koch, Christian, Eldar Sultanow, and Sean Cox. "Divisions by Two in Collatz Sequences: A Data Science Approach." International Journal of Pure Mathematical Sciences 21 (November 2020): 1–13. http://dx.doi.org/10.18052/www.scipress.com/ijpms.21.1.

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The Collatz conjecture is an unsolved number theory problem. We approach the question by examining the divisions by two that are performed within Collatz sequences. Aside from classical mathematical methods, we use techniques of data science. Based on the analysis of 10,000 sequences we show that the number of divisions by two lies within clear boundaries. Building on the results, we develop and prove an equation to calculate the maximum possible number of divisions by two for any given a Collatz sequence. Whenever this maximum is reached, a sequence leads to the result one, as conjectured by

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Nikolaychuk, Anatoliy. "Supplement to the Collatz Conjecture." JOURNAL OF ADVANCES IN MATHEMATICS 15 (December 1, 2018): 8120–32. http://dx.doi.org/10.24297/jam.v15i0.7876.

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For any natural number was created the supplement sequence, that is convergent together with the original sequence. The parameter - index was defined, that is the same tor both sequences. This new method provides the following results:  All natural numbers were distributed into different classes according to the corresponding indexes; The analytic formulas ( not by computer performed routine calculations) were produced, the formulas for groups of consecutive natural numbers of different lengths, having the same index; The new algorithm to find index for any natural numb

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T M, Nishad. "Mathematical Proof of Collatz Conjecture." International Journal of Mathematics Trends and Technology 67, no. 7 (2021): 178–82. http://dx.doi.org/10.14445/22315373/ijmtt-v67i7p521.

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8

Ren. "Reduced Collatz Dynamics Data Reveals Properties for the Future Proof of Collatz Conjecture." Data 4, no. 2 (2019): 89. http://dx.doi.org/10.3390/data4020089.

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Collatz conjecture is also known as 3X + 1 conjecture. For verifying the conjecture, we designed an algorithm that can output reduced dynamics (occurred 3 × x+1 or x/2 computations from a starting integer to the first integer smaller than the starting integer) and original dynamics of integers (from a starting integer to 1). Especially, the starting integer has no upper bound. That is, extremely large integers with length of about 100,000 bits, e.g., 2100000 − 1, can be verified for Collatz conjecture, which is much larger than current upper bound (about 260). We analyze the properties of thos

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KANDASAMY, W. B. VASANTHA, ILANTHENRAL KANDASAMY, and FLORENTIN SMARANDACHE. "The 3n  p Conjecture: A Generalization of Collatz Conjecture." Journal of Ultra Scientist of Physical Sciences Section A 29, no. 2 (2017): 83–88. http://dx.doi.org/10.22147/jusps-a/290207.

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Ashok, Joshi B. "Number Set Theory and Collatz Conjecture." International Journal of Mathematics Trends and Technology 55, no. 3 (2018): 196–99. http://dx.doi.org/10.14445/22315373/ijmtt-v55p525.

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Dissertations / Theses on the topic "Conjecture de Collatz"

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Stroup, David A. "Collatz’s Problem and Encoding Vectors." University of Akron / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=akron1145048595.

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Ibrahim, Ahmed Abdoulkarim. "Monogénéité et systèmes de numération." Thesis, Besançon, 2016. http://www.theses.fr/2016BESA2039.

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Cette thèse est centrée autour de la monogénéité de corps de nombres en situation relative puis à la conjecture de Collatz.\newline Premièrement on détermine l'ensemble de classes des générateurs de l'anneau des entiers des certaines extensions relatives de corps de nombres, en utilisant l'algorithme de Gaál & Phost et le logiciel PARI/GP. La deuxième partie propose différents formulations d'une généralisation de la conjecture de Collatz, aux entiers p-adiques. On étudie ensuite le comportement de suites analogues dans le cadre d'anneaux d'entiers de corps de nombres<br>This thesis are cen

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Yang, Chun-Ming, and 楊峻明. "A Survey on the Collatz Conjecture." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/56615877745463510078.

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碩士<br>國立臺灣大學<br>數學研究所<br>100<br>This thesis surveys some fundamental results about the Collatz Conjecture, including viewpoints in probability, and an equivalent statement in 2-adic numbers. At the end of the thesis, we see some phenomena via programming and define the magnification ratio of n for further development.

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Books on the topic "Conjecture de Collatz"

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Fleming, Danny. How to Prove The Collatz Conjecture. Lulu.com, 2004.

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Book chapters on the topic "Conjecture de Collatz"

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Yolcu, Emre, Scott Aaronson, and Marijn J. H. Heule. "An Automated Approach to the Collatz Conjecture." In Automated Deduction – CADE 28. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79876-5_27.

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AbstractWe explore the Collatz conjecture and its variants through the lens of termination of string rewriting. We construct a rewriting system that simulates the iterated application of the Collatz function on strings corresponding to mixed binary–ternary representations of positive integers. Termination of this rewriting system is equivalent to the Collatz conjecture. To show the feasibility of our approach in proving mathematically interesting statements, we implement a minimal termination prover that uses the automated method of matrix/arctic interpretations and we perform experiments where we obtain proofs of nontrivial weakenings of the Collatz conjecture. Finally, we adapt our rewriting system to show that other open problems in mathematics can also be approached as termination problems for relatively small rewriting systems. Although we do not succeed in proving the Collatz conjecture, we believe that the ideas here represent an interesting new approach.

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Honda, Takumi, Yasuaki Ito, and Koji Nakano. "GPU-Accelerated Verification of the Collatz Conjecture." In Algorithms and Architectures for Parallel Processing. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11197-1_37.

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Kari, Jarkko. "Cellular Automata, the Collatz Conjecture and Powers of 3/2." In Developments in Language Theory. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31653-1_5.

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4

Lopez, Andri. "Collatz Conjecture Proved." In Current Topics on Mathematics and Computer Science Vol. 2. Book Publisher International (a part of SCIENCEDOMAIN International), 2021. http://dx.doi.org/10.9734/bpi/ctmcs/v2/9638d.

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Conference papers on the topic "Conjecture de Collatz"

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Ren, Wei, and Ruiyang Xiao. "How to Fast Verify Collatz Conjecture by Automata." In 2019 IEEE 21st International Conference on High Performance Computing and Communications; IEEE 17th International Conference on Smart City; IEEE 5th International Conference on Data Science and Systems (HPCC/SmartCity/DSS). IEEE, 2019. http://dx.doi.org/10.1109/hpcc/smartcity/dss.2019.00382.

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Shukai Qin, Zhenyu Wang, Yonghong Wang, and Kaijie Xu. "A Method of JavaScript Path Obfuscation Based on Collatz Conjecture." In 2015 12th Web Information System and Application Conference (WISA). IEEE, 2015. http://dx.doi.org/10.1109/wisa.2015.56.

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Aljassas, Hamad Mousa A., and Sreela Sasi. "Performance Evaluation of Proof-of-Work and Collatz Conjecture Consensus Algorithms." In 2019 2nd International Conference on Computer Applications & Information Security (ICCAIS). IEEE, 2019. http://dx.doi.org/10.1109/cais.2019.8769514.

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Ito, Yasuaki, and Koji Nakano. "A Hardware-Software Cooperative Approach for the Exhaustive Verification of the Collatz Conjecture." In 2009 IEEE International Symposium on Parallel and Distributed Processing with Applications. IEEE, 2009. http://dx.doi.org/10.1109/ispa.2009.35.

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Ren, Wei, Simin Li, Ruiyang Xiao, and Wei Bi. "Collatz Conjecture for 2^100000-1 Is True - Algorithms for Verifying Extremely Large Numbers." In 2018 IEEE SmartWorld, Ubiquitous Intelligence & Computing, Advanced & Trusted Computing, Scalable Computing & Communications, Cloud & Big Data Computing, Internet of People and Smart City Innovation (SmartWorld/SCALCOM/UIC/ATC/CBDCom/IOP/SCI). IEEE, 2018. http://dx.doi.org/10.1109/smartworld.2018.00099.

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Ito, Yasuaki, and Koji Nakano. "Efficient exhaustive verification of the Collatz conjecture using DSP48E blocks of Xilinx Virtex-5 FPGAs." In Distributed Processing, Workshops and Phd Forum (IPDPSW). IEEE, 2010. http://dx.doi.org/10.1109/ipdpsw.2010.5470837.

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