Convergence of the Collatz Sequence

  • Anatoliy Nikolaychuk Los Angeles City College.
Keywords: Collatz Conjecture


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:

  1. All natural numbers were distributed into six different classes;
  2. The properties of index were found for the different classes;
  3. 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


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

How to Cite
Nikolaychuk, A. (2019). Convergence of the Collatz Sequence. JOURNAL OF ADVANCES IN MATHEMATICS, 17, 19-33.