Proof to the Collatz conjecture

Discussion in 'Alternative Theories' started by Sean Gilligan, Jul 13, 2022.

  1. DaveC426913 Valued Senior Member

    Messages:
    18,891
    Brilliant!

    I happen to have Python installed. Maybe I'll run some submission requests from Michael345.
     
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  3. BdS Registered Senior Member

    Messages:
    512
    Some upgrades v1.1
    While I'm learning Python

    Output:

    Enter a seed number X: 9663
    28990
    14495
    ...
    9038141
    27114424
    13557212
    6778606
    ...
    4
    2
    1
    Seed Number X = 9663 | X Seed Length = 4
    X Highest = 27114424 | X Highest Length = 8
    Even Steps = 118
    Odd Steps = 66
    Total Steps = 184
     
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  5. DaveC426913 Valued Senior Member

    Messages:
    18,891
    Cool. Bonus marks if you can plot the output as a graph!

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    This one is actually done in Python!

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    https://ultimatetheorem.blogspot.com/2020/08/visualization-of-collatz-conjecture_10.html
     
    Last edited: Jul 21, 2022
    BdS likes this.
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  7. phyti Registered Senior Member

    Messages:
    732
    James R;

    dictionary:
    peer-reviewed) vt
    evaluate something as an expert: to assess an article, piece of work, or research as an expert on the subject

    There are no experts, only people with more experience than others.
    Peer reviewed journals are typically biased, assuming only people associated with eduational or scientific organizations are capable of critical thinking. Many expect to gain copyrights to the submitted material.

    If anyone is interested in a solution to this 'recreational math' problem, here is a pdf.
     

    Attached Files:

  8. DaveC426913 Valued Senior Member

    Messages:
    18,891
    The paper is dated only five weeks ago.

    Are we expected to accept that this is has been reviewed and accepted as a formal proof?

    This is an opinion. Hard to claim what others are thinking without telepathy.

    Still, regardless of whether the opinion is warranted, it's not justification for not submitting one's work to a peer-review, since a review would certainly be capable of finding errors if there were some.

    Not submitting one's work to a peer review process is - at the very least - a tacit admission that the paper probably has holes in it big enough for one's peers to find (otherwise, what's the harm?).
     
    Last edited: Jul 21, 2022
  9. phyti Registered Senior Member

    Messages:
    732
    The paper has been revised a few times over the years, to make it comprehensible for the average reader with basic math skills, and correcting errors.
    It's an opinion based on attempted submissions!
    If the 'experts' have the ability to critique submissions, why don't they solve the problems?
    I'm open to opinions by readers who understand the problem.
     
  10. BdS Registered Senior Member

    Messages:
    512
    output:

    Enter a seed number X: 69
    208 EVEN
    104 EVEN
    52 EVEN
    26 EVEN
    13 ODD
    40 EVEN
    20 EVEN
    10 EVEN
    5 ODD
    16 EVEN
    8 EVEN
    4 EVEN
    2 EVEN
    1 ODD
    Seed Number X = 69 | X Seed Length = 2
    X Highest = 208 | X Highest Length = 3
    Even Steps = 11
    Odd Steps = 3
    Total Steps = 14
    Consecutive Even Steps = 4, 3, 4
    Consecutive Odd Steps =

    There is never any consecutive odd steps. Because as soon as X is odd then you times by 3, X always becomes odd again, then when you add 1 you make it even... ?
     
  11. BdS Registered Senior Member

    Messages:
    512
    Seed Number X = 6325874123658987 ... 88745566321456987 | X Seed Length = 206
    X Highest = 1897762237097 ... 36698964370962 | X Highest Length = 207
    Even Steps = 928
    Odd Steps = 154
    Total Steps = 1082
    Consecutive Even Steps = 634, 6, 2, 5, 2, 5, 2, 2, 2, 2, 5, 2, 2, 2, 2, 4, 2, 2, 4, 3, 2, 2, 2, 3, 2, 2, 2, 3, 3, 5, 2, 2, 3, 5, 2, 4, 3, 4, 2, 2, 4, 2, 3, 2, 2, 2, 4, 2, 2, 2, 3, 5, 5, 2, 2, 7, 2, 3, 2, 2, 6, 2, 2, 6, 3, 3, 3, 3, 4, 3, 2, 3, 4
    Consecutive Odd Steps =

    Not sure why when I enter very long numbers its always starts with a high amount of consecutive even steps? the longer the X number length the greater the first even consecutive steps value. Maybe a limitation to handling large numbers?
     
  12. Neddy Bate Valued Senior Member

    Messages:
    2,546
    Yes, that sounds correct.

    Interesting. Also, it appears that 7 is the maximum number of even consecutive steps after the first large number of even consecutive steps is done. At least that is how it looks from your examples.
     
  13. Neddy Bate Valued Senior Member

    Messages:
    2,546
    BdS,

    Just for fun, try multiplying the odd numbers by 1.5 and then adding 0.5. That will allow some odd numbers to lead to other odd numbers, which will give you some results in the Consecutive Odd Steps = results. It may take forever though, so be careful not to melt your cpu!
     
  14. Neddy Bate Valued Senior Member

    Messages:
    2,546
    Since the rule (odd * 3) + 1 always produces an even outcome, we know the next step will be to divide by 2. So...

    ((odd * 3) + 1) / 2
    (odd * 1.5) + 0.5

    So the rule (odd * 1.5) + 0.5 will ultimately result in the same outcome. But it allows us to track how many consecutive odd steps happen, just for reference.
     
  15. BdS Registered Senior Member

    Messages:
    512
    Not sure whether it is interesting or just a technical limitation in calculating long numbers.
    At first I thought this line "if (int(X) % 2) == 0:" used to check if X is currently odd or even was having a problem parsing the long numbers. I changed it to "if (int(str(int(X))[-1]) % 2) == 0:" to only look at the last digit of X and determine if X is odd or even from the last digit. It produces the same results with both lines, so now I'm not sure whats causing it.

    It's working with natural integer numbers so to change it to use decimals is too much effort

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    load python copy paste the code, you'll just need to get the indentations sorted out, because the website is trimming the leading spaces/tabs on the beginning of every line.
     
  16. Michael 345 New year. PRESENT is 72 years oldl Valued Senior Member

    Messages:
    13,077
    Talking about long numbers

    Don't know how many phone numbers on telephone communication systems

    Indonesia has started to register sim card to phone's IMEI number so it will not work in another phone

    Asked friend over in Bali to buy sim card for me and gave photo of passport

    Friend went to sim card selling shop. When my details were checked shop gave friend new sim card and friend sent to me

    I always put own phone number in the phone. If it gets mislaid call own number and might hear it to track down

    Number on sim card friend given was / is same as number I had / used 5 years agol

    Guessing shop recreated my old number registered it to new device (my upgraded phone) and since NOW REGISTERED will not work in any other phone

    Think of the number of locals with phones all the tourist who use a local number on holiday and then keeping check no phone numbers are duplicated and where it was last used

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