You keep saying the same thing, but the example you give doesn't seem to conform to the usual definition of sample size determination.
I don't think it is possible to do what you are asking for. It sounds like you want to find a sample size N such that you can test future samples of size N (non-parametrically?) against an original sample and conclude that the distributions come from the same population.Testing whether two samples come from the same population is one of the fundamental issues in statistics. There are dozens of tests that you can choose from to determine that "they are the same". You can use tests to compare means, medians, variances, rank-sums, and more. However, you HAVE to specify a test because each test has a different power.
Good luck.
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