Abstract
A general algorithm is developed for a specific algebraic operation on integer numbers carried out iteratively. The operation is shown pictorially by a chain-necklace diagram. The properties of such diagrams are mentioned. Two special cases, namely Collatz's and Nollatz's conjectures, are discussed in detail. The former conjecture gives a full-length sequence only for restricted numbers. A new generalized conjecture is stated and some logical thoughts are given.
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