TY - JOUR AU - Nikolaychuk, Anatoliy PY - 2019/07/23 Y2 - 2024/03/29 TI - Convergence of the Collatz Sequence JF - JOURNAL OF ADVANCES IN MATHEMATICS JA - JAM VL - 17 IS - SE - Articles DO - 10.24297/jam.v17i0.8336 UR - https://rajpub.com/index.php/jam/article/view/8336 SP - 19-33 AB - <p>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:</p><ol><li>All natural numbers were distributed into six different classes;</li><li>The properties of index were found for the different classes;</li><li>For any natural number was constructed the bounded sequence of increasing numbers,</li></ol><p>&nbsp;&nbsp;&nbsp; that is convergent together with the regular Collatz sequence.</p> ER -