/sci/ - Science & Math » Thread #13310288

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Anonymous Tue 22 Jun 14:38:17 2021 No.13310288 View Reply Original Report

Quoted By: >>13310299 >>13310301 >>13310320 >>13310344 >>13310387

I have a question. Is this mathematic procedure equivalent to the collatz conjecture and is it new or already known about?
For integer n.
If n divided by 3 has no remainder, divide n by three.
If n divided by 3 has remainder 1, n = 2n+1
If n divided by 3 has remainder 2, n = 3n+3
N will always return to 1 if you repeat this procedure on n.

My French Celestial girlfriend from the other universe told me that procedure several months ago and Im just wondering if it's new and or if it's valid? If it is new and valid then please officially name it the French Celestial Girlfriend conjecture. Thanks lol.

Anonymous

Anonymous Tue 22 Jun 2021 14:42:01 No.13310299 Report

Quoted By: >>13310305

>>13310288
>collatz conjecture
Not this shit again. Newsflash: nobody fuckin cares about the collatz conjecture, and you shouldn't either.

Anonymous

Anonymous Tue 22 Jun 2021 14:42:25 No.13310301 Report

Quoted By:

>>13310288
An example. 4 has remainder 1 so:

2•4+1=9
9 had remainder 0 so
9/3 = 3
3/3 had remainder 0 so
3/3= 1
Tadaa

Anonymous

Anonymous Tue 22 Jun 2021 14:44:22 No.13310305 Report

Quoted By:

>>13310299
But it's interesting.
Lol.

Anonymous

Anonymous Tue 22 Jun 2021 14:50:48 No.13310320 Report

Quoted By: >>13310323 >>13310369 >>13310398

>>13310288
For this sequence it's trivial that it goes to 1

>Case 1: n = 3k
3k -> k
>Case 2: n = 3k+1
3k+1 -> 6k+3 -> 2k+1
>Case 3: n = 3k+2
3k+2 -> 9k+9 -> 3k+3 -> k+1

As you can see in all possible numbers you are guarenteed to quickly get a number smaller than the one you started with. That is unless k=0 but then your are in the 1-3 loop.

Anonymous

Anonymous Tue 22 Jun 2021 14:52:28 No.13310323 Report

Quoted By: >>13310398

>>13310320
Is it different from the collars conjecture though?
Is there any necessity you are seeing that it must be one?

Anonymous

Anonymous Tue 22 Jun 2021 14:58:30 No.13310344 Report

Quoted By:

>>13310288
Let me know if anybody here finds a counter example or proof that it can't be countered thanks.

Anonymous

Anonymous Tue 22 Jun 2021 15:04:45 No.13310369 Report

Quoted By: >>13310398

>>13310320
But you didn't prove that it must necessarily return to 1 so it is the same as collatz so far lol.

Anonymous

Anonymous Tue 22 Jun 2021 15:13:56 No.13310387 Report

Quoted By: >>13310423

>>13310288
>With 0 remainder, make the number smaller
>With remainder 1, make the number divisible by 3 that will reduce overall value after division by 3
>With remainder 2, make the number divisible by 3 that will yield a remainder of 1 after division
Yes, it will always converge to 1

Anonymous

Anonymous Tue 22 Jun 2021 15:16:42 No.13310398 Report

Quoted By: >>13310423

>>13310323
>>13310369
Suppose you have a sequence
a_1 -> a_2 -> a_3 -> ...
that never hits 1.

Consider the set
{a_1, a_2, a_3, ...}
By the well-ordering principle it has a minimum a_k.
Now look at the sequence that starts at this minimum
a_k -> a_{k+1} -> a_{k+2} -> ...
Clearly no element in this sequence is smaller than a_k or it wouldn't have been a minimum of the set.

But >>13310320 proves that the start value can't be minimum of a sequence unless the start value is 1.
Contradiction therefore a sequence that never hits 1 doens't exist.

Anonymous

Anonymous Tue 22 Jun 2021 15:24:29 No.13310423 Report

Quoted By: >>13310437

>>13310398
>>13310387
What about A^n - B^n - 1 divided by n.
Where A is n/2+.5 and B is n/2-.5.

Is n always pseudoprime or prime if the expression divides evenly?

3^5 - 2^5 -1 /5 divides even and 5 is psuedoprime/prime.

She gave me that one in July 2019.call it the french celestial psuedoprime formula.

Anonymous

Anonymous Tue 22 Jun 2021 15:27:50 No.13310437 Report

Quoted By:

>>13310423
Solve your own damn problems. If you think they're neat, don't spoil the fun you could be having by searching online for an answer. Go ask her for guidance if you need it

Anonymous

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Anonymous Tue 22 Jun 2021 15:29:42 No.13310443 Report

Quoted By:

The Collatz conjecture seems to be true in the case of the resolution on OP's image.

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