# Questions tagged [collatz-conjecture]

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

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### Collatz sequence but multiplying by a large odd number rather than $3.$ What is the simplest way to prove that a sequence goes off to infinity?

Under the Collatz rules: $n\to 837n+1$ if $n$ is odd $n\to n/2$ if $n$ is even. What is the simplest argument/proof to show that there is a Collatz sequence with a starting number that goes off to ...
• 20.7k
1 vote
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### 7 for 5n+1 series diverges to infinity?

Write an odd integer in the "modified" binary form as $2^m - 1$ and apply 5n+1 (similar to applying the rules of original 3n + 1) to it: \begin{align} n &= 2^m - 1 \\ ...
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### Reasoning about the Collatz conjecture, multiple infinitely growing trees that never overlap? [closed]

I have been pondering the Collatz conjecture recently as a mental exercise, and have run into a problem that has to do with proving that an iteratively growing tree of odd positive integers will ...
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### A chaotic function related to the $3x+1$ problem? (Li-Yorke and the Collatz problem)

Let $x$ be an infinite binary string. Define the function $f(x)$ mapping $x$ to the Cantor set of $I = [0,1]$ as: $$f(x) = \sum_{n=0}^{\infty} \frac{2 x_n}{3^{n+1}}$$ where $x_n$ are the ...
108 views

### Collatz conjecture and prime numbers [closed]

With the intention of understanding how prime numbers contribute to the numerical results we get when we perform any possible numerical calculation (also on real numbers), since they are those natural ...
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1 vote
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### What's The Minimum Number Of Prime Factors Needed To Replace "3x+1" With Any Linear ("mx+b") Function And Still Work Like The Collatz Conjecture?

Apologies; I know there are a few assumptions used to pose this question, namely: 1): That yes, any mx+b function can work like the infamous "3x+1," problem... ...Provided, that you give it ...
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### For each integer $k,$ does there exist a $k-$tuple of primes, $(p_n)_{n=1}^{k},$ s.t. for each $n,\ p_{n+1}=2p_n- 1$ or $p_{n+1} =2p_n+1?$

For each $k\in\mathbb{N},$ does there exist a $k-$tuple of primes, $(p_n)_{n=1}^{k},\$ such that for each $n,$ the following is satisfied: $p_{n+1} = 2p_n- 1\$ or $p_{n+1} = 2p_n + 1?$ If yes then ...
• 20.7k
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### Is the number 3 in the Collatz conjecture arbitrary?

One of the most famous conjectures in mathematics is the Collatz conjecture also known as $3n+1$ but my question is why we multiply the odd number by 3? I get that the conjecture probably wants to ...
• 6,598
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### Does this mean that there are no non trivial cycles in the Collatz Conjecture?

I am a grade 9 student who is fascinated with the Collatz Conjecture. I tried to 'prove' that the $4-2-1-4$ cycle is the only cycle that exists. I am aware that there is a huge chance that this is ...
1 vote
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1 vote
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### Do the self-similarities of a fractal function govern its convergence properties?

Let the graph of a function take a fractal form, such as the following representation of the Collatz conjecture topologically conjugated to the interval $[\frac12,1)\to[\frac12,1)$ In this example, ...
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### Collatz Conjecture Interpretation?

Another way to interpret the Collatz conjecture is to say that "playing the game" will always arrive at 2^n. The natural numbers can be rearranged into "rails" of each odd number ...
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### An argument that the value of m in a Collatz conjecture 2-cycle is subject to the same constraints as for a 1-cycle.

Question: Is the reasoning of the following argument valid? Objective: To derive a constraint on the permissible number of total divisions by 2, here referred to as $m$, for a Collatz 2-cycle ...
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