Occurrence rate per bit for any control parameter on the logistic map over integers

We have been investigating behaviors of the logistic map over integers for constructing a pseudorandom number generator with the map. In the presented paper, we will give a 0/1-occurrence rate per bit for values by the logistic map over integers, and discuss suitable bit positions of a bit extraction for getting a pseudorandom bit sequence. First, we will show characteristic behaviors of occurrence rates of values by the map. Second, we will indicate any control parameter are classified into four types which have the distinguished 0/1-occurrence rate patterns. Third, we will show the 0/1-occurrence rate per bit for elements of a sequence generated by the map experimentally. Fourthly, we will introduce a part of the proof for the 0/1-occurrence rate per bit in the low-order bits. Finally, we will suggest suitable bit positions to be extracted for generating a pseudorandom bit sequence.