Distribution of the loops on the logistic maps over integers for the control parameter

We are interested in a distribution of the loops on the logistic map over integers where the control parameter is less than 4. When the control parameter is equal to 4, we have already presented that we can classify a loop on the map over integers into one of the loops on the map over real domain with the same period. In this present paper, we investigate loops on the map over integer with the control parameter is less than 4 by using exhaust search. We show a distribution of these loops and classify them.