# 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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### Why problem with simple formulation is so hard?

If you ever heard about Collatz conjecture, you know that it is understandable even for middle school students, but no one has solved it yet. The problem is to prove or to disprove that starting with ...
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### Application of the Collatz conjecture

I'm very curious about the Collatz conjecture, also known as the $3n+1$ problem, mainly due to its rather simple formulation and beautiful visualizations. After all, Erdős himself said that "...
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### Switches (binary) and dominoes in a “Collatz-universe”

Imagine in a "Collatz-universe" that is discrete and a complex system is buildt up of switches that can either be on or off. How can I make a comparison between physical switches and dominoes in ...
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### Collatz conjecture, Tao-Collatz remainder and mod n.

Collatz conjecture is equivalent to $n\times 3^{k} = 2^{ak+1} - TCR$ where, for me, $k$=odd steps, and $ak+1$=even steps. Note that total steps = k +( ak+1) steps. Some numbers have the same total ...
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### Polynomial extension of Collatz graph… does it converge finitely?

Let $\Bbb Z[2^{-1},2^{-1/2},2^{-1/4,\ldots}]$ be the ring of dyadic rationals extended to include dyadic powers of $2$. Then let $2^{\nu_2(x)}$ extend the 2-adic valuation to dyadic powers of $2$ (...
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### Found a formula for generating all numbers in all possibilities of all cycle lengths

yo, I'm about to spread some new knowledge about the collatz conjecture. Not sure if this has been shown before or not, but here: https://en.wikipedia.org/wiki/Collatz_conjecture#Cycles it states that ...
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### a question about the Collatz conjecture (relation of smallest number in a cycle and minimal cycle-length)

I've only done a bit of research on the current findings, not sure if anyone here can answer this. Q1: I just haven't been able to find, has it been shown yet that a it is ...
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### Infinite Number of Infinite Fractions From Hailstone Sequences? (Non-Optimized Collatz)

Starting with some number, you can generate the hailstone sequence from it. In the case of 3, the (finite) hailstone sequence of it is $[3,10,5,16,8,4,2,1]$. Placing them in a continued fraction like ...
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### Where is my Collatz conjecture proof wrong?

I am amateur and don't have very good understanding of mathematical proving. My proof is so simple i don't believe noone thought of this before. But I am so blinded by the hope it is correct, that I ...
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### Are there nontrivial subsets of the complex unit circle satisfying the multiplicative Jacobi identity?

Let $a^{(b^c)}\times b^{(c^a)}\times c^{(a^b)}=1$ Then a set $S$ satisfies the multiplicative Jacobi identity if this is true for all $a,b,c\in S$. $S=\{1\}$ satisfies the identity. $S=\{0\}$ doesn'...
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### How do p-adic fields degenerate for non-prime $p$?

How do p-adic fields degenerate for non-prime $p$? Let $d(x,y)$ be the inverse of the highest power of $4$ that divides $\lvert x-y\rvert$ Then let $\Bbb Z_4$ be the completion of $\Bbb Z$ under ...
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### Collatz conjecture undecidable from the general case?

There are known results that generalized version of Collatz conjecture is undecidable. I wonder why special case of it still can be decidable? Isn't general case should apply results to all special ...
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### Bitlength probabilities of the shortcut Collatz map

If my calculations are right the probability that the next number in Collatz'sequence has increased its bitlength is equal to $31.25 \%$ Bitlength meaning; the length from a fixed position of least ...
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### Collatz conjecture: $2^{m-1}(6n-3)$ is not part of any cycle

My original method was different from the method shown here. Instead of working my way backward through the iterations as below, I worked my way forward. I choose against doing that here despite of it ...
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### Irritating “proof” of the Collatz Conjecture

I recently stumbled across this self-proclaimed proof of the Collatz Conjecture. It seems very irritating to me that this very hard conjecture is supposedly proven by using very basic counting ...
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### $3n+1$ graph and shared vertices

I found this somewhere on the web: Theorem. The total number of vertices for $n$ squares that share exactly one common vertex is given by the formula $f(n) = 3n + 1$. Proof. Each of the $n$ squares ...
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### Literature request: Papers by Charles C. Cadogan.

I am looking for three papers on the Collatz Conjecture by Charles C. Cadogan. The Annotated Bibliography II (Lagarias) lists these three as: "Charles C. Cadogan (2000), The 3x+ 1 problem: towards a ...
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### Does anyone know where I can get a copy of R. P. Steiner, “A theorem on the Syracuse problem”?

R.P. Steiner. "A theorem on the Syracuse problem". In: ed. by D. McCarthy and H. C. Williams. Congressus numerantium; 20. Proceedings of the 7th Manitoba Conference on Numerical Mathematics and ...
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### Is this Algorithm's Result concerning Collatz Sequences provable?

I have searched the www for this little algorithm and its result thoroughly, but it was nowhere to be found, do you know if my observation is provable? The Algorithm: Step 1: Select an arbitrary ...