This is a pretty cool example of confirmation bias. I was 100% sure the rule was a sequence of numbers that were all powers of some base... (2, 4, 8 - 16, 32, 64 - 3, 9, 27 - 5, 25, 125 - all got a "yes"), but it turned out to be something much simpler/different. It's like if you turn into a certain news channel every day and always see stories about [group of people] doing [thing you disapprove of], you might think that there was something wrong or inferior about [group of people] that causes them to do [thing you disapprove of], rather than something more subtle.
I was of the same opinion. But I was worse than you. I believed that the rule was "each nth number is the nth power of the first one, with n=[1,2,3]". Hence, 2^1, 2^2=4, 2^3=8. I tried several. 3,9,27; 5;25;125; 128; 16384; 2097152. All yeses. Then I tried 1,1,1. I got a "no". But the amount of positive evidence toward my hypothesis was overwhelming. I thought that was a bug.