Convergence of the Collatz Sequence

  • Anatoliy Nikolaychuk Los Angeles City College.
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:

  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.

Downloads

Download data is not yet available.

Author Biography

Anatoliy Nikolaychuk, Los Angeles City College.

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

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.

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.)

Published
2019-07-23
How to Cite
Nikolaychuk, A. (2019). Convergence of the Collatz Sequence. JOURNAL OF ADVANCES IN MATHEMATICS, 17, 19-33. https://doi.org/10.24297/jam.v17i0.8336
Section
Articles