I meant the latter. I think the question is fine. It can lead to a good discussion, similar to what we are having in this thread. It has been a long time (almost 20 years), but I remember that most interviewers who asked this seemed to be convinced that the output they had seen with their compiler version was the correct answer. What could be a nice and relevant discussion, especially considering that some classes of bugs and security issues result from it, was seen only as a trivia quiz by the interviewers, with the expectation of an answer that was incorrect, no less.

Your phone screen story is quite nice. When I read your question, I would have answered with successive doubling as well. In fact, I faced the same question at an AWS interview a long time ago. The question was mathematically the same question but formulated differently. I answered with the doubling solution too, which leads to an O(log n) time solution, asymptotically. Your interviewer's immediate objection to your squaring solution seems like a major failure in their intuition. When I read your solution, purely by intuition, that is, without resorting to any rigorous reasoning, I felt: wow, that's interesting, your solution would land on the zero region in merely O(log log n) time. Why didn't I think of it? I think your solution should spark interest rather than dismissal in a curious person. Of course, the binary search after that to find the exact transition point blows up the time consumed back to O(log n).

Once again, thanks for these really interesting comments!