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

AI Thread Summary
The discussion centers on the Modified Collatz Conjecture and whether it always ends in 1, 5, or 17. Participants debate the validity of calculations involving the formula 3x - 1, with one asserting that starting from 6 leads to a known sequence, while starting from 7 creates a loop involving 5. The Collatz conjecture remains an unsolved problem in mathematics, with experts having struggled to find a definitive solution for decades. Some suggest that the conjecture could be tweaked to yield new results, but the overall consensus is that it remains unresolved. The conversation highlights the complexity and intrigue surrounding this mathematical puzzle.
Dries vanlandschoot
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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?
 
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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).
 
Collatz conjecture. Look up in Wikipedia.unsolved problem in math
 
6, 3, 8, 4, 2, 1, 2, 1....?
 
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Dries vanlandschoot said:
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...
 
Drakkith said:
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.
 
Finding a looping example to the original collatz rules will disprove it as a theorem.
 
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.
 
17 is interesting (slightly); it increases and then loops back to itself. And, yes, some end at 5.

1710310378062.png
 
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... and still unsolved!
 
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DaveE said:
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.
 
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