Talk:Collatz conjecture

Adding a visualization for the mapping (rather than convergence)

https://kentslaney.github.io/ideal-bassoon/

I'm interested in adding a visualization from the above URL to the article (probably the base 3 version), but I'm new to contributing here and wanted to double-check the original research requirements and whatnot before writing the JavaScript to export it properly to GIF. Is there anything I should know before posting? What would be an appropriate sequence length? Here's a watermarked screen recording for 27. Kslaney (talk) 18:54, 1 December 2025 (UTC)

Git provided repo wiki for extended presentation, visualization is specific method, and what uses yours Finite-state machine? Processing, which peculiarity or property related conjection did it highlight? MashiraV (talk) 19:38, 12 July 2026 (UTC)

Collatz graph redirects to Clollatz conjecture.

It definitely needs it's own article, and it's certainly doable. Hlopov Eremei (talk) 05:41, 30 June 2026 (UTC)

Which algebra? I'm not directly interested in the material; specialists tend to try to use induction on numbers. Arithmetic pseudorandom number generators are a closely related field to statistics, so my expectations are different. The collaborative task is the development of distributed computing and numerical processors, but with targeted personal attention, the expected group is small, and intellectual development in this area is quite limited.

In the related field of diaphantic equations, I prefer to study them using cybernetics and ergodicity methods; any rational manifestation signals an expansion of the information pool. MashiraV (talk) 23:18, 12 July 2026 (UTC)

@MashiraV uuuuuuh Hlopov Eremei (talk) 04:31, 13 July 2026 (UTC)

Please add the published corrigendum to reference 22

I request an update to reference 22 in the “k-cycles” subsection. Disclosure: I am Xinjun Wang, the person acknowledged in the corrigendum for identifying the error and for discussions concerning its correction. I am therefore requesting review by an independent editor rather than editing the article directly. The current reference links only to Christian Hercher’s original 2023 paper. The official Journal of Integer Sequences article page now states that a corrigendum exists: Official article page: https://cs.uwaterloo.ca/journals/JIS/VOL26/Hercher/hercher5.html Official corrigendum PDF, dated June 14, 2026: https://cs.uwaterloo.ca/journals/JIS/VOL26/Hercher/corrigendum.pdf The corrigendum states that the derivation of an inequality in the proof of Theorem 21, at the bottom of page 14 of the original article, contained an error, and it provides a replacement argument. I respectfully request the following changes: Retain the citation to the original 2023 paper. Add the official 2026 corrigendum to reference 22. If appropriate, revise the relevant sentence to read: “Hercher extended the method further and, with a correction published in 2026, proved that there exists no k-cycle with k ≤ 91.” Suggested additional citation: Hercher, Christian (June 14, 2026). “Corrigendum to Article 23.3.5: There are no Collatz-m-Cycles with m ≤ 91”. Journal of Integer Sequences. https://cs.uwaterloo.ca/journals/JIS/VOL26/Hercher/corrigendum.pdf Thank you for reviewing this request. Mathlover678 (talk) 07:34, 4 August 2026 (UTC)

@Mathlover678: I have added the corrigendum to the citation, broadly in line with your suggestion. I will leave it to someone else to decide whether to implement the text edit you suggest. Thanks. --JBL (talk) 17:35, 4 August 2026 (UTC)

Declining to fix the text, it says approximately what is already being said already (I think). -- Sohom (talk) 15:31, 17 September 2026 (UTC)

Collatz conjecture has been refuted, approved by Lean, but it was a Lean bug

Though that seems pretty recent, it’s been confirmed through Lean proof automaton (but actually is wrong) see https://lawrencecpaulson.github.io//2026/07/30/Collatz.html

Probably worth updating the article with a mention on that point, though guidance on how to tackle that kind of claim novel proof in WPEN would be nice if I have to do it myself. Thank in advance for your feedback. Psychoslave (talk) 08:27, 5 August 2026 (UTC)

I also thought this was notable, and added it to the article yesterday. See Collatz conjecture#In proofs of correctness. The references are not great, mostly pointers to discussions of the event. If better references become available they should be updated. LouScheffer (talk) 10:53, 5 August 2026 (UTC)

I would remove this, because in formal logic, once you have obtain false you can prove (or disprove) any proposition. The guy who found a bug in Lean just wanted to play with it and do some trolling... ~2026-50738-92 (talk) 17:47, 18 September 2026 (UTC)

Proposed addition: Collatz-type maps on primes

I would like to suggest a short addition concerning a recently published family of prime-based Collatz-type maps.

For transparency, I am the author of the cited paper, so I have a conflict of interest and am not proposing to add the material directly to the article. I would appreciate an independent editor assessing whether the result is sufficiently relevant and due for inclusion.

The published paper is motivated from the the OEIS sequences A365048 and A367479 I contributed. Studied a family of Collatz-type iterative maps defined on the prime numbers. In these maps, the branch of the iteration is selected according to the residue of the current prime modulo 6, and the resulting value is mapped to a nearby prime. Necessary conditions for sufficiently large cycles and conditions for agreement between parameterized variants were derived, while universal termination of the maps remains conjectural.

Source: Najeem Ziauddin, “A Family of Hailstone Maps on the Primes”, International Journal For Multidisciplinary Research, Vol. 8, Issue 4, 2026. DOI: 10.36948/ijfmr.2026.v08i04.85803. Najeemz (talk) 11:18, 17 August 2026 (UTC)