mersenneforum.org 3n+1. a.k.a. The Collatz Conjecture.
 User Name Remember Me? Password
 Register FAQ Search Today's Posts Mark Forums Read

2022-11-05, 17:27   #23
science_man_88

"Forget I exist"
Jul 2009
Dartmouth NS

100000111000102 Posts

Quote:
 Originally Posted by mathwiz Try to think of it this way: Reasoning about different $$kn+c$$ sequences is all well and good, and you can use a finite number of them to show the conjecture holds up to a certain $$n$$ limit. But if you want to use this approach to show the conjecture holds for all $$n$$ then you'll need an infinite number of $$k$$ and/or $$c$$ to do it.
Okay sure. $f^2(n+2y)=f^2(n)+3y$ though for odd n

Last fiddled with by science_man_88 on 2022-11-05 at 17:30

2022-11-07, 10:05   #24
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

3·23·149 Posts

Quote:
 Originally Posted by mart_r and I might add the pertinent sequence A076227 here for further reading.
Thanks for sharing that. Getting those numbers is a 1-day work with a single core, silly pari script. Getting to 2^68 may be a week work (the time doubles with any bitlevel, similar to our TF bitlevels, because at every level b+1 you have to test all remaining classes x from the level b (mod 2^(b+1)), plus all classes x+2^b (mod (2^b+1)).

What is time-costly is to crunch all those remaining sequences, to see they terminate. Some of them are "millions", so the process will take time, even if you have a lot of computers, and even if each step is almost instant (division by 2 is cutting the last zero, in binary, and multiplication by 3 is just a shift and add).

My advice is, don't spend time with Colatz. Not only my advice, but from people who know what they say. Unless you are some genius mathematician, like Terrence Tao, or have that spark of genius like some of my colleagues had, you will only waste precious years of your life. It is catchy, because it looks so simple. Calculations like these, however, lead nowhere, unless you can find a counterexample (which is not probable, many mathematicians believe the conjecture is true).

2022-11-07, 17:19   #25
xilman
Bamboozled!

"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across

89·131 Posts

Quote:
 Originally Posted by chalsall Algebra is to Calculus as Chess is to Go.
Apples are to oranges as strawberries are to pineapples.

I will leave you to stew fruitfully for a while before explaining why.

2022-11-07, 17:37   #26
xilman
Bamboozled!

"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across

89×131 Posts

Quote:
 Originally Posted by LaurV My advice is, don't spend time with Colatz. Not only my advice, but from people who know what they say. Unless you are some genius mathematician, like Terrence Tao, or have that spark of genius like some of my colleagues had, you will only waste precious years of your life. It is catchy, because it looks so simple. Calculations like these, however, lead nowhere, unless you can find a counterexample (which is not probable, many mathematicians believe the conjecture is true).
+1

I spent a cpu year or so back in my naive youth.Likely a core-minute or few these days, thanks to Moore.

This one is only going to be solved by deep mathematics about which we barely have a clue right now.

A parellel might be FLT, which is also deceptively easy to state and yet remarkably difficult to prove.

 Similar Threads Thread Thread Starter Forum Replies Last Post RMLabrador Miscellaneous Math 12 2022-12-26 18:58 Steve One Miscellaneous Math 21 2018-03-08 08:18 MattcAnderson MattcAnderson 16 2018-02-28 19:58 MattcAnderson MattcAnderson 4 2017-03-12 07:39 nibble4bits Math 1 2007-08-04 07:09

All times are UTC. The time now is 13:23.

Sat Feb 4 13:23:27 UTC 2023 up 170 days, 10:52, 1 user, load averages: 0.92, 0.88, 0.87

Copyright ©2000 - 2023, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.

≠ ± ∓ ÷ × · − √ ‰ ⊗ ⊕ ⊖ ⊘ ⊙ ≤ ≥ ≦ ≧ ≨ ≩ ≺ ≻ ≼ ≽ ⊏ ⊐ ⊑ ⊒ ² ³ °
∠ ∟ ° ≅ ~ ‖ ⟂ ⫛
≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘ ∏ ∐ ∑ ∧ ∨ ∩ ∪ ⨀ ⊕ ⊗ 𝖕 𝖖 𝖗 ⊲ ⊳
∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟
¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣ … ⋯ ⋮ ⋰ ⋱
∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ
𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎𝜍 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔