# Questions tagged [collatz-conjecture]

For questions about the iterated map $n \to 3n+1$ if $n$ is odd and $n \to \frac n2$ if $n$ is even, and its generalizations.

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### Question re: Collatz Conjecture

Disclaimer: I'm not a mathematician and for the most part I do not understand what, exactly, it takes to mathematically prove anything. That is where this question comes from. Why can't the Collatz ...
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### Is this single Collatz rule useful?

I have thought of a single simple rule for Colatz conjecture that is slightly different to the normal one. Here it is: $$f:(a,b)\rightarrow (3a+\gcd(a,b),b)$$ Then the Colatz conjecture can be written ...
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### Collatz, better terminology than "total stopping time"?

In the Collatz conjecture, the total stopping time is the number of iterative applications of the collatz map on a number n that is needed to get to the result 1. Now, the total stopping time is not ...
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### "3n + 1 problem" variant, using (n/2 + 3)

Background Variant "3n + 1 problem" Consider a mapping similar to the original "3n + 1 problem" (Collatz conjecture): $n → n/2 + 3$ for even n (variant rule due to +3) $n → 3n + 1$...
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### Can someone explain these groups of linear patterns in the dropping times of Collatz Sequences? Could this lead to a proof?

Please buckle in because this may be a long post, but I think it will be necessary to help the reader understand three things: How this data was generated. How the data is grouped into different '...
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### Is it possible to find closed form of the Collatz conjecture? [closed]

So recently I was thinking about converting the recurrent definition of Collatz conjecture into a closed-form expression, which would map any $n,\space n\in\mathbb{N}$ to the $n^{th}$ iteration of the ...
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### What does it take to find integer solutions to this exponential division equation?

Consider this equation where $a$ and $b$ are positive integers. $$k = \frac{2^a - 1}{2^{a+b} - 3^b}$$ This equation has the trivial solution $k=1, a=1, b=1$. How would I find more solutions, or show ...
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### Jacobsthal numbers occurring in reduced cobweb plot for the Collatz Problem

I have been working on the Collatz problem for a while now, and have made this efficient cobweb plot function for it, where it automatically does all the dividing by two and always returns an odd ...
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### Collatz conjecture but with $\ 3n-1\$ instead of $\ 3n+1.\$ Do any sequences go off to $\ +\infty\$?

Collatz conjecture but with $\ 3n-1\$ instead of $\ 3n+1.\$ Do any sequences go off to $\ +\infty\$?  Background (not necessary to answer my question): Considering the following operation on ...
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### Collatz Conjecture: Reasoning about the possible divergence of a collatz sequence

I've been thinking about the possibility of a divergent collatz sequence for the Collatz Conjecture. In other words, the possibility that neither a trivial nor non-trivial cycle is ever reached. If ...
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### What does Terry Tao mean by exponential separation

Tao wrote in his blog post (in the fourth last paragraph): Thus we see that any proposed proof of the Collatz conjecture must either use transcendence theory, or introduce new techniques that are ...
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### Collatz Conjecture: For a cycle where the maximum odd integer is $x_{max}$, does it follow that $x_{max} < 3^n$

I am working on understanding the upper limit in the case where a non-trivial cycle exists for the Collatz Conjecture. Is the following reasoning valid for establishing that the maximum odd integer in ...
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