A note about the chaotic behavior of the Wald Interval for a binomial proportion

It is well known that the coverage probability of the standard Wald confidence interval to estimate a binomial proportion has a very erratic behavior as a function of the parameters n (sample size) and p (probability of success) . Till now it has been thought that this behavior was "basically unpredictable". Nevertheless, the analysis of this behavior allows to obtain a formula that provides, for a fixed p, all the sample sizes in which the coverage probability decreases sharply from n-1 to n.