In , the 3x + 1  is a special subsemigroup of the multiplicative  of all  rational numbers. The elements of a generating set of this are related to the sequence of numbers involved in the still open  or the “3x + 1 problem”. The 3x + 1 has been used to prove a weaker form of the . In fact, it was in such context the of the 3x + 1 was introduced by H. Farkas in 2005. Various generalizations of the 3x + 1 have been constructed and their properties have been investigated.

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