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.

Author Biography

Anatoliy Nikolaychuk, Los Angeles City College.

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


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.

Guy, R. K. (1983). "Don't try to solve these problems". Amer. Math. Monthly. 90: 35–41. doi:10.2307/2975688. JSTOR 2975688. By this Erdos means that there aren't powerful tools for manipulating such objects.

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.