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]).