Talk:Collatz conjecture

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Collatz-graph is a tree

Collatz-graph is connected and acyclic.

Content:

1.Formulas for forward and backward sequences.

2.Family tree

3.Collatz sequence tree

4.Conclusion.

Exploring other mathematical sequences:

5. (3*N+5)/2^m

6. Juggler sequence

https://sourceforge.net/projects/trial-collatz-proof/ Kavalenka (talk) 13:55, 29 December 2024 (UTC)[reply]

Solution of Collatz Conjecture

If you want to see a solution for Collatz Conjecture, refer to Volume 13 Issue 1 2025, Global Scientific Journal, "Unveiling the mystery of the Collatz Conjecture" by Sandoval Amui. It just takes elementary arithmetic (Geometric progressions) 2804:9188:1:9FBB:64EC:C3BF:D452:DDC3 (talk) 00:01, 13 February 2025 (UTC)[reply]

Semi-protected edit request on 10 March 2025

This edit request has been answered. Set the |answered= parameter to no to reactivate your request.

The article uses the word "begin" in excess. Can we use alternative synonyms please. 204.48.78.190 (talk) 23:07, 10 March 2025 (UTC)[reply]

Not done The word "begin" appears zero times in the article ("beginning" twice). --JBL (talk) 23:45, 10 March 2025 (UTC)[reply]

Application of the Collatz conjecture on decimals

I found that the collatz conjecture can be solvable if the rules are modified. Let's consider it even if the last digit is divisible by 2, unless it's a decimal zero. If not, it's considered odd. So far, the numbers I have found do not end up on a loop or go infinitely. 122.53.180.74 (talk) 12:32, 9 April 2025 (UTC)[reply]

To clarify, I meant the decimal numbers I've found. 122.53.180.74 (talk) 12:37, 9 April 2025 (UTC)[reply]

If the rules are modified, it's not the Collatz conjecture. —Tamfang (talk) 21:49, 9 April 2025 (UTC)[reply]

(p, q)-adic analysis

Max Siegel — a graduate student from the University of Southern California — seems to have put immense effort into developing a new approach to studying the Collatz conjecture.^[1]^[2] I'm not confident enough mathematically to add anything from his dissertation myself, but it may be noteworthy and it appears interesting. Thoughts? Ramanujaner (talk) 21:51, 23 April 2025 (UTC)[reply]

Why's no one answering? His work is in souce [1] and source [2] shows that USC has accepted his thesis. It is quite novel and perhaps worth mentioning, is it not? Ramanujaner (talk) 19:03, 28 April 2025 (UTC)[reply]

Seigel talks about it as perhaps being an interesting jump point. Seigel himself indicates it isn't a proof and while it may be interesting and useful to talk about in a forum devoted to it, neither the talk page nor the article itself is the place for that.Naraht (talk) 13:40, 29 April 2025 (UTC)[reply]

I do not want to burst your bubble, but the work of Max Siegel does not help at all and is a trivial reinterpretation of the problem. I wasted my time having a deeper look into his work after I was convinced by reddits posts that he is not mentally ill. 133.6.130.80 (talk) 01:43, 7 May 2025 (UTC)[reply]

References

^ Siegel, Maxwell Charles (2024-12-03), $\left(p,q\right)$-adic Analysis and the Collatz Conjecture, arXiv, doi:10.48550/arXiv.2412.02902, arXiv:2412.02902, retrieved 2025-04-23
^ "Algebra". Department of Mathematics. Retrieved 2025-04-23.

Hailstone sequences in Prime Numbers

Suggestion to add to reference section

(1) This hailstone operation on odd prime numbers will always reach 3. reference: https://oeis.org/A365048

a(n) is the number of steps required for the n-th odd prime number to reach 3 when iterating the following hailstone map: If P+1 == 0 (mod 6), then the next number = smallest prime >= P + (P-1)/2; otherwise the next number = largest prime <= (P+1)/2. If the condition "(P + (P-1)/2)" is changed to "(P + (P+1)/2)" then some prime numbers will go into a loop. For example, 449 will loop through 2609.

If the condition "(P+1)/2" is changed to "(P+3)/2" then some prime numbers will go into a loop. For example, 5 will go into the loop 5,7,5,7,....

(2) This hailstone operation on prime numbers will always reach 2. reference: https://oeis.org/A367479

a(n) is the number of steps required for prime(n) to reach 2 when iterating the following hailstone map: If P == 5 (mod 6), then P -> next_prime(P + ceiling(sqrt(P))), otherwise P -> previous_prime(ceiling(sqrt(P))); or a(n) = -1 if prime(n) never reaches 2.

note: next_prime(x) is the next prime >= x, and previous_prime(x) is the next prime <= x. Najeemz (talk) 09:46, 22 June 2025 (UTC)[reply]

I think we need stronger sourcing than an OEIS entry to add material like this. OEIS lists a lot of things and I think its only real acceptance standard is mathematical validity. While I think it is reliable for the facts that it lists it doesn't really provide evidence that the material is WP:DUE for this article. —David Eppstein (talk) 22:04, 22 June 2025 (UTC)[reply]

[1] Siegel, Maxwell Charles (2024-12-03), $\left(p,q\right)$-adic Analysis and the Collatz Conjecture, arXiv, doi:10.48550/arXiv.2412.02902, arXiv:2412.02902, retrieved 2025-04-23

[2] "Algebra". Department of Mathematics. Retrieved 2025-04-23.

[1]

[2]