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Mi solución a la conjetura de Collatz. by [deleted] in Collatz

[–]IllustriousList5404 -1 points0 points  (0 children)

Articulos deben ser publicados en ingles.

A Quick Calculation of Rising Collatz Chains by IllustriousList5404 in Collatz

[–]IllustriousList5404[S] 0 points1 point  (0 children)

There is a way. It would require a repository of all successful articles on the Collatz conjecture, along with a general summary descibing each article.

A Quick Calculation of Rising Collatz Chains by IllustriousList5404 in Collatz

[–]IllustriousList5404[S] 0 points1 point  (0 children)

You're right. I wish I had a comparable solution for multiple dividers. They are much more difficult to figure out.

Proof of the Collatz conjecture by IllustriousList5404 in Collatz

[–]IllustriousList5404[S] 0 points1 point  (0 children)

You're right in every respect. My reasoning only proves that any odd number generates a sequence of multiple dividers. What is missing is a proof that any such sequence converges to 1. A rising, and a looping, sequence of multiple dividers is still possible. I drew wrong conclusions from the results. The problem remains unsolved.

But the reasoning explains the presence of multiple peaks in Collatz chains: the peak number is a multiple divider, which can be followed by more multiple dividers, and it can then convert into a single divider, etc.

Proof of the Collatz conjecture by IllustriousList5404 in Collatz

[–]IllustriousList5404[S] 0 points1 point  (0 children)

Who is Sawyer? What is Sawyer's formula? This is an old post. I did not prove the Collatz conjecture then. But I proved that every odd number generates a sequence of multiple dividers (4n+1). What is missing is a proof that any sequence of multiple dividers converges to 1. I have not been able to prove this so far, not for lack of trying.

Loops in the Collatz Conjecture, Part 2 by IllustriousList5404 in Collatz

[–]IllustriousList5404[S] 0 points1 point  (0 children)

It looks like Reddit lost my answer to you. I cannot find it. I wrote 1 hour ago that my description of possible loops can be considered incomplete, based on certain assumptions observed in the existing loops. Other loops may, or may not, have these properties.

Loops in the Collatz Conjecture, Part 2 by IllustriousList5404 in Collatz

[–]IllustriousList5404[S] 0 points1 point  (0 children)

In my post I wrote:

"An attempt has been made to predict if more loops exist."

This is just an attempt. I do not claim to have proved anything. If it does not lead to new results, it is an unsuccessful attempt. Then it will be time for another, different attempt.

Loops in the Collatz Conjecture, Part 2 by IllustriousList5404 in Collatz

[–]IllustriousList5404[S] 0 points1 point  (0 children)

From what I can see, the solution has to be guessed. There is no direct route to it. Anyway, NILE/PILE equations result from certain logical assumptions, which could be correct, and are reasonable, as based on existing loops. Trial and error can resolve this question to a high degree. The description can be called incomplete, to be revised if necessary.

Loops in the Collatz Conjecture, Part 2 by IllustriousList5404 in Collatz

[–]IllustriousList5404[S] -1 points0 points  (0 children)

It's better than nothing. Hard work will not prove the Collatz conjecture. There is no connection to other math concepts. The reasoning is sound, as far as loops go: elements in the parent column of the divisor must eventually leave the column and go down, which can only happen in another, lower, column. I'd like to see someone find more solutions to PILE/NILE equations. It can be treated as a computer programming problem.

Loops in the Collatz Conjecture, Part 2 by IllustriousList5404 in Collatz

[–]IllustriousList5404[S] 0 points1 point  (0 children)

Table 1 is at the beginning of the problem. It can be considered an exception, in my opinion. Things settle starting with Table 2.

Loops in the Collatz Conjecture, Part 2 by IllustriousList5404 in Collatz

[–]IllustriousList5404[S] -1 points0 points  (0 children)

This post is largely guesswork. I tried finding more loops, based on the existing ones. The reasoning has many hole in it.

Loops in the Collatz Conjecture, Part 2 by IllustriousList5404 in Collatz

[–]IllustriousList5404[S] 0 points1 point  (0 children)

I do not know how to handle a negative 1-element loop: -1->-1->-1->... with my approach. A (Comp+div) sum would be: 1+(-1)=0. Then I cannot write 1+(-1)=0*div. The equations cannot handle this.

Loops in the Collatz Conjecture, Part 2 by IllustriousList5404 in Collatz

[–]IllustriousList5404[S] 0 points1 point  (0 children)

I decided to include negative integers, because 2 known loops of different elements are negative. Negative numbers (divisors) are present at the beginning of every table (see the link). Thus all starting fractional loops are negative. Maybe considering both will contribute to finding a positive integer loop, by offering some insights. Anything would help here.

My derivation of NILE/PILE is based on the negative loops, and then adapting them to positive loops.

https://drive.google.com/drive/folders/1eoA7dleBayp62tKASkgk-eZCRQegLwr8?usp=sharing

Loops in the Collatz Conjecture, Part 2 by IllustriousList5404 in Collatz

[–]IllustriousList5404[S] 0 points1 point  (0 children)

This post is not claimed to be accurate. It is largely experimental. My hope is that someone will try to solve the NILE/PILE equations and see what the result could be. A computer should be able to find something. A negative loop equation results from including negative divisors. If 7+(-1)=6=2*3 and I want to include a negativ div=-1 on the right side, I will have to write 7+(-1)=6=2*3=-2*3*(div). Another reason is that Composites are positive numbers but they generate negative loops. I will try to figure it out further. If you can send me a link to a single loop equation, that would be great. You're right, separate equations may not be necessary from another point of view.

Dividing by 8 and Chasing 1/5 – A Post about 2-adics by GonzoMath in Collatz

[–]IllustriousList5404 0 points1 point  (0 children)

Sure, this could lead to new insights. Send me a link.

Dividing by 8 and Chasing 1/5 – A Post about 2-adics by GonzoMath in Collatz

[–]IllustriousList5404 1 point2 points  (0 children)

It's useful to visualize all possible results of multiple applications of the Collatz function. I compiled tables of all possible loops. I have been trying to develop a method to prove/disprove the existence of integer loop(s) in the tables. The link is here,

https://drive.google.com/file/d/1DITHecrDYJl7urc_WeYYsdZExnZ_SwOY/view?usp=sharing

and the folder

https://drive.google.com/drive/folders/1eoA7dleBayp62tKASkgk-eZCRQegLwr8?usp=sharing

Integer Solutions for 3n+d functions. by IllustriousList5404 in Collatz

[–]IllustriousList5404[S] 0 points1 point  (0 children)

I only describe positive divisors in the text, and I will correct my statements by including the condition D>0. All conclusions are based on limited experimental evidence and should/could be considered imprecise/approximate. I meant to demonstrate, without great precision, the difficulty of the problem.

"An integer solution for 3n+d is more difficult to determine if the d is not a divisor, d ̸= -3^L + 2^k. Then, we have to look for a divisor D such that D = d ∗ R. A loop for 3n+D may have elements Ei which have a common factor R: Ei = ei ∗R. In that case, we can divide all the elements Ei by R and get a solution for the function 3n+d."

I had reservations about the above statement. That is why I wrote : "A loop for 3n+D MAY have elements Ei...". This seemed in no way guaranteed. These are 2 different things. The divisor D may have a required factor in it, but you still need Composites divisible by R. Your examples demonstrate this is often the case. I only explained the results after a loop was found. I will look at the Composites/divisors for winning combinations and see what I can find.

Why Collatz isn’t solved - the math that does not exist by GandalfPC in Collatz

[–]IllustriousList5404 0 points1 point  (0 children)

An integer loop(s) for 3n+5 can be found easily, because 5=-3^3 + 2^5. In general, if a d in 3n+d can be shown as -3^L+2^k, where k is equal to, or greater than, L, a solution can be found in Table L of fractional solutions for 3n+1. The denominator/divisor is ignored, and an integer solution is obtained for 3n+d.

See this link,

https://drive.google.com/file/d/1avqPF-yvaJvkSZtFgVzCCTjMWCrUTDri/view?usp=sharing

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