1, 1, 1 was actually the test case that clued me in that n^1, n^2, n^3 couldn't be the right solution.

n=1?

But I totally see why it would cause you to pause and rethink your original idea :).

The point is that it didn't work, so exponentiation was out the window.

My point was that 1,1,1 is 1^1,1^2,1^3 and actually fits the pattern :).

Right - by fitting the pattern but failing the actual criterion, it disproves the consecutive exponents hypothesis.