When you say, "I have a procedure for calculating the minimum sample size required for ensuring a significant result.", do you actually mean something along the lines of  "to increase the likelihood of finding a statistically significant result, assuming the effect actually exists in the population from which the sample was [randomly] drawn?" When working with samples, there are no guarantees of finding an effect if one exists in the population, unless your sample size approaches that of the population; in other words, you simply cannot ensure a [statistically] significant result. All you can do is increase the likelihood of finding one.

Researchers who are concerned about the issue of false negative rates (all really should be) tend to refer to the work of Jacob Cohen - a quick search of your library will reveal some useful sources which you may find helpful.

This question is about R programming and tests of significance as a technology, not statistical philosophy. (And the article is correct in regards to the latter, as well. You should read it before commenting.)