# 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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### Transform Collatz sequence to a strictly decreasing sequence

While playing with numbers, I found that every Collatz sequence $n, T(n), T^2(n), \ldots, 1$ can be associated with a strictly decreasing sequence of integers. The Collatz conjecture asserts that a ...
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### Collatz sequence lengths for Primorials

The primorial $(\#)$ function is defined as the product of first $n$ prime numbers. Is there a simple explanation for the observation that the length of the Collatz sequence for successive primorials ...
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### Let $x=2^{p-1}-1$ be composite, $p$ prime and $3\mid x$. Why $p \mid x$?

Let $x=2^{p-1}-1$ be a composite odd natural number (a "wrong" Mersenne) and $p$ is prime and $3\mid x$. Why $p \mid x$? Does really $p$ always divides $x$? Note: We know that $x$ is a sum of powers ...
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### Collatz extensions

Because, in the basic Collatz algorithm, odds are always transformed into evens (via x=3x+1), and evens are transformed into evens with a probability of .5 (via x=x/2), there will be, on average, 2 ...
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### Collatz function iterates as a Markov chains

In the Collatz Conjecture, the question is wether the sequence of iterates will always reach $1$ for all $n>0$ where $n\in\mathbb{Z^+}$. The formal Collatz function consists of the operations: $n/2$...
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### Is this a valid proof of the Collatz theorem? [closed]

Is this a valid proof of the Collatz Conjecture? For all even numbers x >= 20, if all numbers 1 through x are in Collatz set, show x+1 and x+2 are in set. Then by induction, all positive integers ...
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### Calculate the maximum in the Collatz sequence

Consider the notorious Collatz function $$T(n) = \begin{cases}(3n+1)/2&\text{ if n is odd,}\\n/2&\text{ if n is even.}\end{cases}$$ One of the most important acceleration techniques of ...
272 views

### What is the flaw in this proof of the Collatz Conjecture?

Would love any feedback for this proposed proof of the Collatz Conjecture. (For more details explaining each step, I made a video here: https://www.youtube.com/watch?v=P0F4zbNdbTU ) Ignoring all ...