Sequence puzzle: 3, 9, 27

A twist of the classic sequence game:

A friend asked me to find the rule to this sequence: 3, 9, 27.

I am allowed to suggest other sequences to test if they follow that (unknown to me) rule, to which my friend can say yes or no. Once I think I got the rule I can say it.

Here are the sequences I tried and his answer:

1 2 3 No
3 6 9 No
3 27 81 Yes
9 27 81 Yes
3 9 81 No
3 9 27 81 Yes
81 9 27 3 Yes
-6 -8 -2 Yes
-8 -2 -6 Yes
-2 -6 -8 Yes
3 5 0 No
3 5 10 11 No
3 5 11 No
3 6 11 Yes
19 6 11 Yes
3 5 12 No
5 5 5 No
6 6 6 Yes
pi 4 8 Not Consistent

Can you determine the rule to generate the sequence?

• What does "Not Consistent" mean? (That whatever rule is in play only makes sense when applied to certain sequences, and that isn't one of them?) Commented Jun 19, 2021 at 22:26
• "Not Consistent" probably means that terms need to be integers. Commented Jun 20, 2021 at 8:03
• Observation: Every single example contains a number that is a multiple of 3, except for 5 5 5 (no). This is only about 1% likely, if he were sampling numbers randomly for his examples. I mean it's already obvious he's not, but 3 is still a notable fixation. Commented Jun 22, 2021 at 5:47