A first observation is that there are other cycles if negative integers are allowed in the domain of the function. There is a cycle of period 1 starting from n = -1, and there are cycles of length 3 and 11 starting from n = -5 and n = -17, respectively. Böhm and Sontacchi [13] conjecture that these cycles together with the cycles starting with n = 0 and n = 1 make up the entire set of cycles occurring under iteration of applied to the integers . Several authors have proposed the following conjecture ([13], [28], [41], [67]).
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