Initial values entering into an element zero with period one for logistic maps over integers

In the presented paper, we consider initial values entering into an element `zero´ with period one for logistic maps over integers. First, we derive the logistic map over integers. Second, we describe that only two elements, namely zero and the maximum value in domain of the logistic map, enter into the loop with zero, respectively, for control parameters less than 4. Last, we show that three elements, zero, the maximum value and its half value, always enter into zero for the control parameter equals to 4, and we indicate experimentally that an event that these three initial values only entering into zero has a probability of about two-thirds for any precision. In conclusion, we will obtain a result that the probability that we choose initial values entering into the loop with zero is negligible, if we select a suitable precision for the logistic map over integers by a simple check.