Convergence of the Collatz Sequence
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.
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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.)
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