#Collatz Conjecture Solution

43 messages · Page 1 of 1 (latest)

lilac garden
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Hello! I have a solution to the collatz conjecture, which disproves the theory. My cat helped me find a sequence of numbers which will reach infinity. Although this sounds funny or like a troll, I am being serious, and would really appreciate it if anyone could confirm this.

While I was trying to find a pattern in the conjecture using a polar plot, I got bored and went to some random website to calculate the sequence for a random input number. After having obviously no success with that, I went to refill my water, and my cat sat on my keyboard. He held the 99999 key down for a while. When I got back, I thought it was funny, I tried it, and it apparently had an insane glide.

I experimented further with this. For each 9, the glide goes up by 3 (roughly). This pattern goes on forever. So each time you double the amount of 9s, the glide also doubles.

Very quickly I crashed the online program by putting in a few hundred or so 9s. So i created a java program to test this using BigIntiger and StringBuilders, and I tested all combinations of 9 up until 25,700 digits of 9 long. It quickly passed the highest glide record, and it mostly followed the pattern, though some lengths of 9 go wayyy higher than expected.

I then hit the String input limit so I needed to use a function to act as a string builder. I tested an input of 2.6 Million digits of 9 to start out with, and it went up by about 500,000 - 600,000 digits before starting to come back down. However, it took my computer 2 whole days to calculate this entire sequence.

Therefore, if a few million or billion digits of 9 were input, then this could easily go high enough to loop back to itself. However, my computer isnt good enough for that.

Would this be a proper solution disproving the collatz conjecture? If so then how do I get people to hear me? I made a video and a paper about this but nobody is responding to me. I feel like people think im joking.

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also if you look at the binary values of each number, it makes a weird triangular pattern which I dont understand

spark acorn
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your supposed disproof of the conjecture is that a big number takes a long time to come down to 1, or what?

lilac garden
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not just any big number, most big numbers have a glide of 3 and just act like any number, but this number gets exponentially bigger at a constant rate

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you would see it if you try comparing it to other number sequences

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like a number starting with a ton of 9s in a row will get wayyyyyyyy bigger than it started

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for example: 999999999999999999999999999999999999999999999999 has a max value of 566,774666,856932,966136,362495,035427,855327,725410,461425,781248, which is 566,774,666x bigger than what it started at

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and thats a short sequence of 9s already going extremely high compared to what it started at, almost no other numbers do that, but any sequence of 9s does that

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Average numbers of all size even giant numbers have a glide of 3.
The world record highest glide found is around 2,000
The highest sequence of 9s I tested had a glide of around 866,666

lilac garden
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if this doesnt make sense just try putting a random large number in and then try doing a long amount of 999999999999. You will see the difference

spark acorn
lilac garden
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so every number 1 less than a power of 2 or 1 less than a power of 10 gives a super big number? interesting

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i wonder what the highest form of 2^n-1 was tested

spark acorn
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oh i guess there is

lilac garden
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does this apply to all numbers ^n-1

spark acorn
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even, yes

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that they multiply by 1.5^n before ever seeing an even number

lilac garden
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so if theres a whole bunch of these patterns that get exponential really fast, shouldnt we find the one that has the highest exponential rate and then try a really big version of it?

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i could just make a java program to find that

urban tree
lilac garden
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well if numbers really can shoot up an infinite amount, and theres an infinite amount of numbers that can go that high up, then i dont see why a massive number cant go trillions of steps up before going back down, and find another number that goes that high up

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even if these numbers are super rare, we have a way of testing numbers that are pretty much guarenteed to go that high

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whether it be 10^n-1 or 2^n-1

urban tree
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like 2^n - 1 will go up to 3^n - 1 in 2n steps

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but there's no reason to expect 3^n - 1 won't go back down

lilac garden
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is 2^n-1 always exactly 3^n-1 in 2n steps or does it have variance

spark acorn
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it is always

lilac garden
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bc when i was testing 10^n-1 it would sometimes to way higher than the constant rate i thought it would

spark acorn
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(3n + 1)/2 multiplies a number's distance from -1 by 1.5

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again, this really says nothing about whether it eventually drops to 1
it kind of suggests that it will take longer, but that's not really true because smaller numbers can take much longer than larger numbers

urban tree
lilac garden
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tho im going to experiment with it a little bit bc it sounds like 2^n-1 and 9^n-1 act different

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tho still it should only need a delay of around 186 billion or something to be big enough to loop, and that isnt that much compared to infinite

spark acorn
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its distance from -1

spark acorn
lilac garden
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yeah either that or one to infinite, and for a while i thought 9^∞-1 would have a delay of ∞ though I cant exactly compute that

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well it does but i dont think thats being counted as an answer

urban tree
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idk what I was thinking