The ideas behind Terras's analysis seem basic to a deeper understanding of the problem, so I describe them in detail. In order to do this, I introduce some notation to describe the results of the process of iterating the function . Given an integer n, define a sequence of 0-1 valued quantities by


where . The results of first k iterations of T are completely described by the parity vector


since the result of k iterations is






Note that in (2.5), (2.6) both and are completely determined by the parity vector given by (2.3); I sometimes indicate this by writing (instead of . The formula (2.4) shows that a necessary condition for is that


since is nonnegative. Terras [67] defines the coefficient stopping time to be the least value of k such that (2.7) holds, and if no such value of k exists. It is immediate that


The function plays an important role in the analysis of the behavior of the stopping time function , see Theorem C.
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