I have been wondering if there are any numbers that exist only in their own string of the 3n+1 problem.
I need to explain that better. Basically, when you follow the rules of the conjecture, you end up with a string of numbers, starting with whatever you chose and ending with 1. Example with 995: 995 -> 2986 -> 1493 -> 4480 -> 2240 -> 1120 -> 560 -> 280 -> 140 -> 70 -> 35 -> 106 -> 53 -> 160 -> 80 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1
Basically, I'm wondering if there are numbers that don't appear in strings of any other numbers. So with the example given, we know that 2986, 1493, 4480, 2240, 1120, 560, 280, 140, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1 all don't meet that criteria.
So if you took every single number, then wrote the string of numbers that comes from each number, would any numbers only appear once?