So begin with a sequence of 1 1 1 1 1 1 1 1 1 1. That establishes a baseline cadence of minutes, or hours or whatever. A clock signal if you will.

Then switch to primes. I think anyone looking at that kind of message will figure it out eventually. It can't be mistaken for a natural occurence.

> So begin with a sequence

That is the trick that I was calling out. The intervals are reals, and cannot be made into a sequence. Beginning with a sequence is even worse; what is in evidence (for the aliens) is a set of real intervals. That's what the aliens have to begin with.

Now explain how they get to primes.

If the precision between the intervals is good, how can you not get to primes? Of course the intervals would be real, but there would be a very discernible pattern.

It would stare you in the face, or what am I missing?

I disagree. Sequences of reals are still sequences. So maybe hypothesis one has nothing to do with integers, maybe it's that the intervals are increasing geometrically. You're still going to take ratios and and start having suggestive numbers fall out. "can't just switch ... without explanation". The point is that this putative alien observer would be looking for the explanation. Maybe the first few explanations they come up with are the wrong ones, but they are trivial to check. It's not like it's a research project to reject the Fibonacci hypothesis.So you would still have the right answer on day one.