Convergence of the Collatz Sequence
DOI:
https://doi.org/10.24297/jam.v17i0.8336Keywords:
Collatz ConjectureAbstract
For any natural number was created the supplement sequence, that is convergent together with the original Collatz sequence. The numerical parameter - index was defined, that is the same for both sequences. This new method provides the following results:
- All natural numbers were distributed into six different classes;
- The properties of index were found for the different classes;
- For any natural number was constructed the bounded sequence of increasing numbers,
that is convergent together with the regular Collatz sequence.
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References
Lagarias, Jeffrey C. (1985). "The 3x + 1 problem and its generalizations". The American Mathematical Monthly. 92 (1): 3–23. JSTOR 2322189.
Nikolaychuk, Anatoliy (2018). "Supplement to The Collatz Conjecture". Journal Of Advances in Mathematics, Vol. 15, pp. 8120–8132. ISSN:2347 - 1921.
Guy, Richard K. (2004). ""E17: Permutation Sequences"". Unsolved problems in number theory (3rd ed.). Springer-Verlag. pp. 336–7. ISBN Zbl 1058.11001.
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Roosendaal, Eric. "3x+1 Delay Records". Retrieved 30 June 2017. (Note: "Delay records" are total stopping time records.)
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