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# Talk:3x-1 problem

## Trajectories that eventually hit a power of 2

Regarding "It is very likely that the 3x-1 problem has trajectories that eventually hit a power of 2"... Shouldn't that be "there *are*" such trajectories? For example, the sequence 29, 86, 43, 128, 64, 32, 16, 8, 4, 2, 1, ... would be one. Or am I misunderstanding? Will Nicholes 16:44, 15 February 2011 (UTC)

- You understood it correctly. I think Daniel was trying to make some other point, which I'll have to ask him about. For now, I've corrected the page to the point that you and I are understanding. By the way, a sequence containing 29, 86, 43, 128, ... as a subsequence might be worth adding to the OEIS. Alonso del Arte 17:47, 15 February 2011 (UTC)

- Thanks Alonso. I've found a few interesting 3x+1 related sequences I'm planning to submit; once I'm done with that I will probably submit a couple of interesting 3x-1 related sequences as well (assuming no one beats me to them.) Will Nicholes 18:46, 15 February 2011 (UTC)

- You can take your time. Right now the other contributors seem far more interested in prime numbers. Alonso del Arte 22:49, 15 February 2011 (UTC)

Daniel, I'm sure you realize that numbers of the form

always hit 2^(2n + 1). The 2^k gets divided out in precisely k halving steps. Then the tripling step gets rid of 3 as a denominator in the fraction (or replaces it by 1 if you prefer) leaving us with 2^(2n + 1) + 1. Lastly, the subtraction of 1 gets rid of the second "+ 1," leaving precisely 2^(2n + 1).

What I don't know is if there's a pedagogical purpose to saying "seems to hit ... is this always the case?" If this was a textbook, I figure such a statement would be in the exercises section of the chapter. Alonso del Arte 06:30, 16 February 2011 (UTC)

- I should have figured that one, obviously... — Daniel Forgues 08:37, 16 February 2011 (UTC)