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collatz sequence^2


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15 replies to this topic

#1 phil1882

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Posted 02 March 2014 - 08:24 PM

take a number, greater than 1.

if odd, subtract 1, square it.

if even, divide by 2.

2 -> 1

3 -> 4 -> 2

5 -> 8 -> 4

7 -> 36 --> 9 -> 16 -> 8

11 -> 100 -> 25 -> 576 -----> 9

13 -> 144 ----> 9

will this always hit a power of 2?

 


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#2 bonanova

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Posted 03 March 2014 - 01:55 PM

Spoiler for First guess


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#3 bonanova

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Posted 04 March 2014 - 11:28 AM

Spoiler for With a little more thought ...


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#4 phil1882

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Posted 05 March 2014 - 03:03 AM

i'm fairly certain 27 diverges.

Spoiler for

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#5 plasmid

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Posted 07 March 2014 - 03:14 PM

Still not a solution, but if I could get a better handle on the function
(n x 2a + 1) = m2
it might lead to one.
Spoiler for

Edited by plasmid, 08 March 2014 - 08:09 PM.

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#6 bonanova

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Posted 11 March 2014 - 12:48 PM

Spoiler for Proof that 2^p - 1 (and other numbers) converge

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#7 bonanova

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Posted 12 March 2014 - 06:11 AM

Spoiler for Here are the convergent (and divergent) numbers.


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#8 plasmid

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Posted 12 March 2014 - 08:17 AM

Interesting, but I'm not sure that those formulas cover all numbers that converge, so I don't think you could conclude that a number doesn't converge based on the fact that it doesn't fit any of the described cases that do converge. As an example, 23 converges but I don't think it fits any of those cases.
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#9 plasmid

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Posted 12 March 2014 - 04:11 PM

The following perl program brute-forces an answer to my earlier question, which I think gives a solution, although I'd rather find a way to solve it without brute force.
Spoiler for

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#10 bonanova

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Posted 13 March 2014 - 05:58 AM

Spoiler for Final thoughts

 

plasmid, I went over my stuff tonight and found the number 23 also. That number, and 47 and a few others, converge for a simple reason explained in the spoiler, and I think that makes the list complete. However, I would love to learn of any other mavericks or, even more interestingly, any other generating equation.


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- Bertrand Russell




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