Supplement to the Collatz Conjecture
For any natural number was created the supplement sequence, that is convergent together with the original sequence. The parameter - index was defined, that is the same tor both sequences. This new method provides the following results:
- All natural numbers were distributed into different classes according to the corresponding indexes;
- The analytic formulas ( not by computer performed routine calculations) were produced, the formulas for groups of consecutive natural numbers of different lengths, having the same index;
- The new algorithm to find index for any natural number was constructed and proved.
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