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.
577 questions
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Reference request: a particular generalization of the Collatz problem
This is a reference request; is this particular generalization of the 3ドル\cdot n+1$ problem discussed in literature? What is known about it? Do any specific choices of $m,ドル $a_i$ lead to nontrivial yet ...
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Is the Collatz map algorithmically decidable?
Question: Has it been proven that the following decision problem is algorithmically decidable?
$$
P_\text{Collatz} := \text{Given $n \in \mathbb{N}_+,ドル does the Collatz-Iteration of $n$ eventually ...
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What is the origin and interpretation of this piecewise formula for Rule 54?
I'm researching the properties of the single-cell evolution of ECA Rule 54 and its connection to the Collatz conjecture.
The MathWorld page for Rule 54 1 and OEIS A118108 2 both present (or are ...
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Is there any known finite sequence of positive integers $a_i$ such that 2ドル^{a_k}-3^k$ is a positive proper divisor of $\sum_{i=0}^k 3^i2^{a_k-a_i}$? [closed]
Is there any known finite sequence of positive integers $(a_i)_{i=0}^k$ such that 2ドル^{a_k}-3^k$ is a positive proper divisor of $\sum_{i=0}^k 3^i2^{a_k-a_i}$?
Any nontrivial loop in the Collatz ...
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A good estimate of $S_k$?
Motivation :
In a collatz orbit (of odd numbers) , one of the most reasonable questions to ask are :
Can we keep dividing consecutively by 2ドル^p$ forever ? ($p>1$)
If not, what's the exact number ...
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Are there any linear bounds for the smallest odd element in a nontrivial collatz cycle?
As my original question was closed for reasons I don't understand, I'll just try again: I was trying to get some bounds the for length of nontrivial Collatz cycles.
Now for one of the arguments to ...
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Why do large sequences in the Collatz Conjecture have an even-to-odd ratio of about 1.7? [duplicate]
I was experimenting with the Collatz Conjecture in python, and I created a script that finds the integers with the largest sequence of the Collatz Conjecture in a specified range. What I found ...
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Are all orbits of $f$ Cauchy over the ternary rationals in $\left[\frac12,\frac23\right),ドル over some separable, compact topology?
Question
Are all orbits of $f$ Cauchy in $\left[\frac12,\frac23\right),ドル over some separable, compact topology?
Definitions
Let a 5-rough number be a natural number divisible by neither two nor three.
...