Open AccessConvergence of the Collatz Sequence
Author(s) -
Anatoliy Nikolaychuk
Publication year - 2019
Publication title -
journal of advances in mathematics
Language(s) - English
Resource type - Journals
ISSN - 2347-1921
DOI - 10.24297/jam.v17i0.8336
Subject(s) - mathematics , sequence (biology) , collatz conjecture , natural number , convergence (economics) , bounded function , index (typography) , combinatorics , discrete mathematics , conjecture , mathematical analysis , computer science , genetics , world wide web , economics , biology , economic growth
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.