I think the most common is "X is left as an exercise for the reader", but it looks like both are in use.
Is the "to" variant correct? If not, why?
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I would say the alternatives should be:
It seems to me that "to the reader" modifies "left" whereas "for the reader" could modify reader or it could modify exercise. When left at the end as in the question, then I'd have to suggest that "to the reader" is incorrect.
That is basically a question about diction/meaning, not grammar: perhaps the main reason that the "basic" to has come within the last few decades to be a catchall preposition that can connect practically any two words or phrases, whether the result is awkward, sensible or not. It will not be of much use to try parsing examples. Simply look up and understand their meanings, and then use the word, to or for, that expresses the meaning you want (not wish) to convey.