Does the Modified Collatz Conjecture Always End in 1, 5, or 17?

[Dries vanlandschoot]

Homework Statement

3x+1 =odd. If even x÷2

Relevant Equations

What if we use 3x-1 and x÷2

Did some calculations and with 3×-1 i Always get 5.is this correct?

 

[DaveE]

Umm... What? Please elaborate. Maybe some examples? I don't know what your question is.

But: 3x + 1 = (odd) => 3x + 1 - 2 = (odd) -2, and (odd) -2 = (odd) => 3x - 1 = (odd).

 

[Dries vanlandschoot]

Collatz conjecture. Look up in Wikipedia.unsolved problem in math

 

[DaveE]

6, 3, 8, 4, 2, 1, 2, 1....?

 

[Drakkith]

Did some calculations and with 3×-1 i Always get 5.is this correct?

No. Starting at 6 you get the sequence above in DaveE's post.
Starting at 7 we get: 7, 20, 10, 5, 14, 7...

 

[WWGD]

No. Starting at 6 you get the sequence above in DaveE's post.
Starting at 7 we get: 7, 20, 10, 5, 14, 7...

And there's the proof we won't hit 2. Once we hit the 2nd 7, we'll be looping indefinitely.

 

[jedishrfu]

Finding a looping example to the original collatz rules will disprove it as a theorem.

 

[jedishrfu]

Recent Sciam article on Collatz

https://www.scientificamerican.com/article/the-simplest-math-problem-could-be-unsolvable/

At first glance, the problem seems ridiculously simple. And yet experts have been searching for a solution in vain for decades. According to mathematician Jeffrey Lagarias, number theorist Shizuo Kakutani told him that during the cold war, “for about a month everybody at Yale [University] worked on it, with no result. A similar phenomenon happened when I mentioned it at the University of Chicago. A joke was made that this problem was part of a conspiracy to slow down mathematical research in the U.S.”

The Collatz conjecture—the vexing puzzle Kakutani described—is one of those supposedly simple problems that people tend to get lost in. For this reason, experienced professors often warn their ambitious students not to get bogged down in it and lose sight of their actual research.

 

[DaveE]

17 is interesting (slightly); it increases and then loops back to itself. And, yes, some end at 5.

 

[PeroK]

... and still unsolved!

 

[WWGD]

17 is interesting (slightly); it increases and then loops back to itself. And, yes, some end at 5.

View attachment 341703

Maybe we can tweak it into a new result that this version will end in 1,5 or 17? Just a Wil guess. Someone used to call it the " Law of Small Numbers"; wild guesses from limited data.