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Let's say I ask a question and accept an answer. Then I decide the answer doesn't fully satisfy me and the reason is that my question should be slightly more specific. Is it appropriate to edit the question and then accept a new answer or should I post the edited question separately with a link to the original one?

Example. Let's say I ask for an example of an even number and accept an answer that says $6$ then decide what I wanted to ask was for a power of $2$.

The reason I am asking is somewhat more subtle than the above example. Some time ago I asked for a property of numbers in $\mathbb{N}$ such that we know is satisfied at least by a number but we don't even have a bound for one such number. I now would like to add the condition that this property is such that for any $n\in \mathbb{N}$ we have a way of checking whether $n$ satisfies it.

I've already asked the author of the accepted answer about the edited question in a comment. My doubt would be about what to do if he cannot answer it.

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    $\begingroup$ "Can you"? yes. "Should you"? no. $\endgroup$
    – GEdgar
    Apr 16, 2016 at 15:47
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    $\begingroup$ It is not appropriate to significantly change the content of the question after it's already been answered, since it's wasting the time of the person(s) who already went to the effort of working it out. Ask a follow up question and link to the original for context, and clarify what new information you're adding. $\endgroup$
    – user296602
    Apr 16, 2016 at 19:34
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    $\begingroup$ When this happens to me, I will flag a moderator who will force the original question back. Of course, if you change the accepted answer then that's your business but now your decision to change acceptance will appear odd. Best to simply ask a new question and not anger people who take the trouble to answer your question. $\endgroup$
    – Ron Gordon
    Apr 18, 2016 at 19:12
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    $\begingroup$ There's nothing wrong with just posing a sequence of related questions. They are, after all, different questions, so why obliviate previously existing perfectly good answered questions? $\endgroup$
    – MPW
    Apr 19, 2016 at 3:14
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    $\begingroup$ I would add to the answer that you can edit your old question to add a link to the follow-up one. That way, a reader who found your old question interesting will be able to find the new one as well. $\endgroup$
    – N. Virgo
    Apr 24, 2016 at 9:20

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Because this is a case of progressive insight resulting in a substantially refined question (an algorithm isn't very sensible if no such number exists), I would consider a follow-up question a better approach in this case.

Also because the original question is still interesting with the follow-up in place.

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