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
where
and
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.