Convergence of the Collatz Sequence

Anatoliy Nikolaychuk

doi:10.24297/jam.v17i0.8336

Authors

Anatoliy Nikolaychuk Los Angeles City College.

DOI:

https://doi.org/10.24297/jam.v17i0.8336

Keywords:

Collatz Conjecture

Abstract

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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Author Biography

Anatoliy Nikolaychuk, Los Angeles City College.

855 N Vermont Ave, Los Angeles, CA 90029, Los Angeles City College

References

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Roosendaal, Eric. "3x+1 Delay Records". Retrieved 30 June 2017. (Note: "Delay records" are total stopping time records.)