Coreli

Coreli stand for "Collatz Research Library". Archangelo Corelli.

The Collatz process is a very simple to describre: take any number x, if even do x/2 if odd do (3x+1)/2. Repeat.

Starting from 5: [5, 8, 4, 2, 1, 2, 1, 2, 1, ...].

Starting from 43: [43, 65, 98, 49, 74, 37, 56, 28, 14, 7, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1, 2, 1, ...].

The Collatz Conjecture, unresolved since the 60s, states that, any stritcly positive natural numbers reaches 1.

The appararent simplicity of this problem hides a very difficult mathematical problem. Actually, we believe that this problem has a lot to do with Computer Science. That's why we created Coreli, a library for experimenting and testing hypothesises regarding the Collatz process.

Doc

Coreli's doc is hosted here.

Dev: deploy to pypi

python setup.py sdist
twine upload dist/*

References

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• Jean Berstel, Jr. and Christophe Reutenauer. Rational Series and Their Languages. Springer- Verlag, Berlin, Heidelberg, 1988.

• Jose Capco. Odd Collatz Sequence and Binary Representations. Preprint, March 2019. URL: https://hal.archives-ouvertes.fr/hal-02062503.

• Livio Colussi. The convergence classes of Collatz function. Theor. Comput. Sci., 2011. URL: https://doi.org/10.1016/j.tcs.2011.05.056, doi:10.1016/j.tcs.2011.05.056.

• J.H Conway. Unpredictable iterations. Number Theory Conference, 1972. Zachary Franco and Carl Pomerance. On a Conjecture of Crandall Concerning the qx + 1 Problem. Mathematics of Computation, 64(211):1333–1336, 1995. URL: http://www.jstor. org/stable/2153499.

• Patrick Chisan Hew. Working in binary protects the repetends of 1/3h : Comment on Colussi’s ’The convergence classes of Collatz function’. Theor. Comput. Sci., 618:135–141, 2016. URL: https://doi.org/10.1016/j.tcs.2015.12.033, doi:10.1016/j.tcs.2015.12.033.

• Pascal Koiran and Cristopher Moore. Closed-form analytic maps in one and two dimen- sions can simulate universal Turing machines. Theoretical Computer Science, 210(1):217– 223, January 1999. URL: https://doi.org/10.1016/s0304-3975(98)00117-0, doi:10.1016/ s0304-3975(98)00117-0.

• Stuart A. Kurtz and Janos Simon. The Undecidability of the Generalized Collatz Problem. In TAMC 2007, pages 542–553, 2007. URL: https://doi.org/10.1007/978-3-540-72504-6_49, doi:10.1007/978-3-540-72504-6_49.

• Jeffrey C. Lagarias. The 3x + 1 problem and its generalizations. The American Mathematical Monthly, 92(1):3–23, 1985. URL: http://www.jstor.org/stable/2322189.

• Jeffrey C. Lagarias. The 3x+1 problem: An annotated bibliography (1963–1999) (sorted by author), 2003. arXiv:arXiv:math/0309224.

• Jeffrey C. Lagarias. The 3x+1 problem: An annotated bibliography, ii (2000-2009), 2006. arXiv:arXiv:math/0608208.

• Kenneth Monks. The sufficiency of arithmetic progressions for the 3x + 1 conjecture. Proceed- ings of the American Mathematical Society, 134, 10 2006. doi:10.2307/4098142.

• Terence Tao. Almost all orbits of the collatz map attain almost bounded values, 2019. arXiv:arXiv:1909.03562.

• Riho Terras. A stopping time problem on the positive integers. Acta Arithmetica, 30(3):241–252, 1976. URL: http://eudml.org/doc/205476.

• Günther Wirsching. On the combinatorial structure of 3n + 1 predecessor sets. Discrete Math- ematics, 148(1-3):265–286, January 1996. URL: https://doi.org/10.1016/0012-365x(94)00243-c, doi:10.1016/0012-365x(94)00243-c.

• Günther J. Wirsching. The dynamical system generated by the 3n + 1 function. Springer, Berlin New York, 1998.