Algorithm to exclude false positives

Question

I want to do the following: For a list of some hundreds participiants where some measure belongs to each participant, I want an algorithm that determines at which sample size a t-test or such would yield that the samples are not significantly different (e.g. by comparing the means) - as it should be. I was thinking at starting with a sample size n (say n = 10) and if the nullhypothesis that the mean of the samples is only unsignificantlly different is discarded, I would try a bigger and bigger sample size. But this seems to me a too crude of an approach. Is there a more elegant/efficient way to do this?