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Say I want the first N numbers generated by PRNG to be some list [n1, n2, n3, n1, nx...]. Is there any way to accomplish this (basically find the appropriate seed for the PRNG?) in some efficient manor, short of bruteforcing it?

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What's the point? If you have a random number generator g, you can write your own random number generator h that returns n1,n2,... for the first N calls and thereafter returns the same as g.

But to answer your question: if the PRNG is any good, then you will have to brute-force it, which will be impractical if N is more than about four or five.

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