Talk:Collatz conjecture

0 and negative numbers = 1 is never reached

A006577: Number of halving and tripling steps to reach 1 in '3x+1' problem, or -1 if 1 is never reached.

If n is 0 or negative, then A006577(n) = -1.

0: 0, 0, 0, 0, 0, 0, 0, ...

-1: -2, -1, -2, -1, -2, -1, ...

-3: -8, -4, -2, -1, -2, -1, -2, -1, ...

-5: -14, -7, -20, -10, -5, -14, -7, -20, -10, -5, -14, -7, -20, -10, -5, ...

-6: -3, -8, -4, -2, -1, -2, -1, -2, -1, ...

-9: -26, -13, -38, -19, -56, -28, -14, -7, -20, -10, -5, -14, -7, -20, -10, -5, -14, -7, -20, -10, -5, ... 2A00:6020:A123:8B00:3913:1297:6B6B:CCEF (talk) 13:19, 14 December 2023 (UTC)

The article could have used a visualization in base 3 (in trinary calculation)

This article could have used an animation for trinary numbers, say, a .GIF of 4975 being broken down. 81.89.66.133 (talk) 13:01, 2 February 2024 (UTC)

Please clarify and expand that. —Tamfang (talk) 19:56, 27 March 2024 (UTC)

Worth mentioning h(x)=(7x+2-(5x+2)cosπx))/4 ?

This function is mentioned in the French page and avoid testing parity. [[1]] Japarthur (talk) 09:02, 8 March 2024 (UTC)

See the section Collatz_conjecture#Iterating_on_real_or_complex_numbers. --JBL (talk) 17:50, 8 March 2024 (UTC)

Semi-protected edit request on 16 March 2024

BEFORE: Eliahou (1993) proved that the period p of any non-trivial cycle is of the form AFTER: Eliahou (1993) proved that the period p of the next candidate for a non-trivial cycle is of the form

Idk, im not a mathematician, but i read the paper cited and the p that is used here seems to be only the current (1993) best candidate for a loop above m=2**39, but below 2**48 . As it is earlier mentioned, this region has already been investigated, so not only the original statements "any" false, but the big letter equation is also irrelevant. 89.223.151.22 (talk) 07:55, 16 March 2024 (UTC)

 Not done: From what I understand, the paper states that all non-trivial cycles (if any exist) have a cardinality of the form $301994a+17087915b+85137581c$. Your proposed change would imply that a non-trivial cycle that is not the first one to be found might not have a cardinality of that form, which contradicts the theorem proved by the paper. Saucy^{[talk – contribs]} 10:43, 25 April 2024 (UTC)

It’s solved by Gaurangkumar Patel

Collatz Conjecture Solution The Collatz conjecturela is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1.https://en.wikipedia.org/wiki/Collatz conjecture The solution in simple words, all number made out of 1. Like 1=1 2=1+1 3=1+1+1 4=1+1+1+1| 5=1+1+1+1+1 Etc. I am saying not only 1 is repetitive but 4,2,1 is repetitive. 3x+1 in if x=1 then, 3(1)+1= 4, then as per rules 4/2 =2 then 2/2=1 means 4,2,1 Now if x=2 then 3(2)+1=7 then as per rules 3(7)+1=22, then 22/2= 11, then 3(11)+1= 34 then 34/2= 16, 16/2=8, 8/2=4, 4/2=2, 2/2=1. Now if x=3 then 3(3)+1=10, 10/2 = 5, 3(5)+1=16, 16/2=8, 8/2=4, 4/2=2, 2/2=1| If we see in all solutions starting from one of the small integers 4,2,1 is repetitive. Because in x=3 there is ans 5. allAll ISSN:3006-4023 (Online),JournalofArtificiallntelligence GeneralScience (JAIGS)86 GaurangkumarPatel20894 (talk) 07:01, 5 April 2024 (UTC)

WP:NOR Felixsj (talk) 15:37, 5 April 2024 (UTC)

Yes. This talk page is only for discussing improvements to the article, which can only be based on reliably published sources. If you believe you have a solution, this is not the place for publicizing it, nor for getting it published, nor for encouraging people to explain why it does not constitute a valid proof. —David Eppstein (talk) 20:03, 5 April 2024 (UTC)

But it’s true data it’s about giving right information to public we don’t fool them. GaurangkumarPatel20894 (talk) 02:21, 7 April 2024 (UTC)

The way to get information to the public is to publish it in respectable academic journals, first. —David Eppstein (talk) 03:26, 7 April 2024 (UTC)

Felixs are David are right. Bubba73 ^{You talkin' to me?} 03:37, 7 April 2024 (UTC)

Semi-protected edit request on 8 April 2024

Explaining Convergence

While a mathematical formula or explanation-based proof may yet be difficult, it is possible to explain the underlying mechanism responsible for convergence by transforming the problem statement as followsCollatz Conjecture - Explaining the Convergence: a) For an odd number N, (3N+1) is always an even number, therefore the next step will always be a division by 2. Both these steps can be considered as a single operation, i.e. (3N+1)/2.

b) Sequential multiplication steps (3N+1)/2 may be considered as a single operation until an even number is obtained.

c) Sequential division (N/2) may be considered as a single operation until an odd number is obtained.

With the help of these transformations, it can be observed that for a starting odd number series, (2i-1)*2ⁿ-1,

a) Multiplication steps result in the even series (2i-1)*3ⁿ-1

b) The resulting superset of even values is represented by either {(6i-4), i ∈ ℕ} or by {(6i-1)*3ⁿ-1 and (6i-5)*3ⁿ-1, i & n ∈ ℕ}

c) The next set of odd numbers obtained through division steps is represented by {(6i-5)*2²ⁿ-1]/3 and (6i-1)*2²ⁿ⁺¹-1]/3, i & n ∈ ℕ}

While mathematical traceability between the starting odd number and the next odd number obtained in step (c) above is difficult to maintain, this approach still helps understand the underlying mechanism leading to convergence.

To explain this, one may begin from the other end of the problem and perform (2N-1)/3 operations on an even series (instead of (3N+1)/2 on a starting odd series). The starting even series E₁=1*2^2n-1, results in a set of odd numbers which can be multiplied by 2ⁿ or 2^n-1 if the odd number belongs to series {6i-5} or {6i-1} respectively. Sequential performance of these inverse operations results in a hierarchy of even series as shown in this exhibit Hierarchy of Even Series. Rakesh Vajpai (talk) 06:22, 8 April 2024 (UTC)

We cannot use this material without a published reliable source. Personal blogs are not reliable sources for this purpose. —David Eppstein (talk) 07:15, 8 April 2024 (UTC)

Thanks David. I am not a mathematician and have no idea what it takes for such articles to be published. I may not even be interested in doing so as my focus is on making these aspects known to people who may be attempting to solve this problem. I have no interest in claiming any credit for the insights. Therefore, if it cannot be published here, I will understand and will leave it at that. Thanks once again. Cheers Rakesh Vajpai (talk) 12:49, 10 April 2024 (UTC)

Collatz function for some known megaprimes

The project math101.guru/en/category/collatz/ contains the logs of the Collatz function for some of the top known megaprimes and their vicinities (can not add link due to spam filter). The data currently cover 15 out of Top 17 known megaprimes (except for #7 and #8 discovered in 2023). There are also some interesting graphs with numerical data available that may be added to other graphs in the article. As far as I could say, such big numbers (>45 in total) have never been tested for the validity of the Collatz conjecture. Re2000 (talk) 07:06, 14 April 2024 (UTC)

You may be interested in this thread. --DaBler (talk) 14:22, 15 April 2024 (UTC)

The numbers they discuss there are infinitesimal compared with the tested numbers in the project above. E.g., they discuss 2^6,000,000 -1, whereas the largest known megaprime tested in the project was 2^82,589,933 − 1. There is nothing of value in the discussion you mention, though it is definitely asking a valid question - "what is the largest number tested for the validity of the Collatz conjecture?" Re2000 (talk) 14:33, 18 April 2024 (UTC)

They calculated 2^10,000,000 + 1 in 48 minutes. --DaBler (talk) 18:57, 18 April 2024 (UTC)

This is still 2^72,589,033 smaller than the largest tested number. 87.236.191.246 (talk) 06:06, 19 April 2024 (UTC)