All Questions
Tagged with collatz-conjecture proof-explanation
13 questions
4
votes
1
answer
283
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Variant of the Collatz Conjecture - Why is the following happening:
I am a web developer that programs in PHP which is limited to large math calculations.
I am also a math enthusiastic that likes learning math through problems that seem simple (but are anything like ...
- 1,425
1
vote
1
answer
221
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Collatz Conjecture - analyzing ending possibilities and the need to prove loops
According to the rules of the Collatz Conjecture if $n$ is odd then execute $3n + 1$ and when $n$ is even execute $n/2$. Repeat until (supposedly) reaching $n = 1$.
examples:
$1 → 4 → 2 → 1$
$13 → ...
- 1,425
3
votes
1
answer
176
views
Collatz Conjecture confusion about the following patterns:
According to the rules of the Collatz Conjecture if $n$ is odd then execute $3n + 1$ and then when $n$ is even execute $n/2$ and then we are supposed to repeat, however for the purpose of this ...
- 1,425
1
vote
1
answer
137
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Collatz Conjecture, can the following skip a prime number?
Following my previous questions at: Collatz Conjecture, why an increment of $+6$ in the following? and Collatz Conjecture, why a rate of change of $*4$ in the following?
Following the rules of the ...
- 1,425
1
vote
1
answer
102
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Collatz Conjecture, why an increment of $+6$ in the following?
Following my previous question at: Collatz Conjecture, why a rate of change of $*4$ in the following?
Following the rules of the Collatz Conjecture, in this experiment I have created a list of all odd ...
- 1,425
1
vote
2
answers
121
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Collatz Conjecture, why a rate of change of $*4$ in the following?
Following the rules of the Collatz Conjecture, in this experiment I have created a list of all odd numbers until $33333$. The list includes 3 columns, such as in the following sample:
A) Starting Odd ...
- 1,425
0
votes
0
answers
101
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Collatz Conjecture: Am I understanding the Chain Equation from Simons & de Weger (2005) correctly? Is this inequality valid?
I was thinking through the Chain Equation from this paper by Simons & de Weger on the Collatz Conjecture.
The Chain Equation is an equation which is only true if a nontrivial cycle (a cycle other ...
- 10.1k
3
votes
0
answers
166
views
Collatz Conjecture: Unclear on one step in the proof for Lemma 10 of Simons & Weger (2005)
I have been reading the Simon & Weger (2005) paper on the Collatz Conjecture.
Let:
$u$ be a natural number.
$\delta = \dfrac{\log 3}{\log 2}$
$p_n/q_n$ be the $n$th convergent to $\delta$
$T(u)...
- 10.1k
2
votes
1
answer
121
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Collatz Conjecture: Unclear on the last argument for Lemma 8 in the paper by Simon & Weger 2005
I am reading through the 2005 paper by Simons and Weger on the Collatz Conjecture.
Lemma 8 has the following conclusion:
$$\delta K < K +L < 1.000001\delta K$$
I am clear on most of the argument....
- 10.1k
3
votes
0
answers
156
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Collatz Conjecture: Understanding why for a given $K, L$, there are only a finite number of solutions
I am reading through this paper by
by Simon & Weger regarding the Collatz Conjecture.
I am stuck on the reasoning at the end of 2.2
Let:
$n$ be a natural number.
$T(n) = \begin{cases}
\frac{1}{2}...
- 10.1k
3
votes
1
answer
259
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Collatz Conjecture: Understanding the Chain Equation (2.1) in the proof by Simons & de Weger (2003)
I am trying to understand the observations that make up the Chain Equation (2.1) from this paper by Simons & de Weger (2003).
I am not clear on the first two observations in the statement of the ...
- 10.1k
4
votes
1
answer
196
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How would I go about proving the following statement?
For all $x \in \mathbb{N}$ and $y \in \mathbb{N}$,
$$ Q= \frac{2^x-3^x}{3^x-2^{x+y}}$$
the only time Q is a natural number and odd is when $(x,y)=(1,1)$.
I've been trying to solve this for a ...
- 43
2
votes
3
answers
4k
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Collatz conjecture pattern (3n + 1 problem).
I have a pattern I found in Collatz Conjecture I want to share. Afterwards, I would like to know, if I could try harder at this pattern (I am stuck), if it could lead to a proof. Or it would just be ...
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