Odd numbers cause double plus one additional passengers to board. So a cycle starting with 3 is a bit different.

3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 -> 4 ...

You misread it, too, did you? 😉

7→22→11→34→17→52→26→13→40→20→10→5→16→8→4→2→1→4→2→1→4→2→1...

Edit: also, 9→28→14→7...

And, 15→46→23→70→35→106→53→160→80→40→20→10→5→16→8→4→2→1...

Or even, 19→58→29→88→44→22→11→...

And lest we forget, 3→10→5→16→8→4→2→1...

That covers every odd number below 20. Want me to do 21 and 25, too? Perhaps 27?