Hello there,

Some of you may have heard of this by another name as there are several people associated with the long history of this problem. For those that never heard of this i will give a short introduction.

There are some simple rules to this problem as follows:

1. Pick a number from 1 to any number and it must be a whole number like 1,2,3, 21,56, etc.

2. If the number is even, divide by 2.

3. If the number is odd, multiply by 3 and add 1 (hence the general name of this problem).

4. After you get a result, repeat steps 2 and 3 using the result from either step 2 or step 3.

First i will give an example of a "loop".

Start with 1. It is odd, so 1*3+1=4.

Now 4 is even, so divide by 2 to get 2.

Now 2 is even, so divide by 2 to get 1.

We started with 1 and got 1 as a result, so if we keep going we will just repeat the 1,2,4 sequence.

That is what is known as a loop. Once we hit a loop we are done because it will just keep repeating.

Now for a slightly bigger example but still fairly short.

Start with 26, it's even so divide by 2 getting 13.

That's odd so 13*3+1=40

That's even so 40/2=20, then 20/2=10, then 10/2=5.

That's odd so 5*3+1=16.

That's even so 16/2=8, then

8/2=4, then 4/2=2, then 2/2=1, then 1*3+1=4

so we hit the 1,2,4 loop i outlined above so we are done working with the number 26.

Now for the conjecture...

"No matter what number you start with (step 1) you always end up with the 1,2,4 loop".

It's still just a conjecture because it has not been proven or unproven to date.

If you want to play around with this and see if you can prove or disprove it, be forewarned it has been proven true up to the number 2^68 so you'd have to start there if you wanted to use trial and error as has been done getting to that number.

Good luck if you do.

I thought this was interesting because it's such a simple problem but possibly not possible to prove or disprove.

As a side note, there is a scientist that is somewhat casually trying to show that the universe evolves from simple functions like this not from elementary particles. What is amazing about this function is it could generate huge structures before finally settling to that 1,2,4 sequence. if you pick a larger number something above 6000 you can get a wild variation, but even with smaller numbers like 27 you get 111 results before it settles to the 1,2,4 sequence which is still kind of lengthy.

Try it out it's kind of cool

Some of you may have heard of this by another name as there are several people associated with the long history of this problem. For those that never heard of this i will give a short introduction.

There are some simple rules to this problem as follows:

1. Pick a number from 1 to any number and it must be a whole number like 1,2,3, 21,56, etc.

2. If the number is even, divide by 2.

3. If the number is odd, multiply by 3 and add 1 (hence the general name of this problem).

4. After you get a result, repeat steps 2 and 3 using the result from either step 2 or step 3.

First i will give an example of a "loop".

Start with 1. It is odd, so 1*3+1=4.

Now 4 is even, so divide by 2 to get 2.

Now 2 is even, so divide by 2 to get 1.

We started with 1 and got 1 as a result, so if we keep going we will just repeat the 1,2,4 sequence.

That is what is known as a loop. Once we hit a loop we are done because it will just keep repeating.

Now for a slightly bigger example but still fairly short.

Start with 26, it's even so divide by 2 getting 13.

That's odd so 13*3+1=40

That's even so 40/2=20, then 20/2=10, then 10/2=5.

That's odd so 5*3+1=16.

That's even so 16/2=8, then

8/2=4, then 4/2=2, then 2/2=1, then 1*3+1=4

so we hit the 1,2,4 loop i outlined above so we are done working with the number 26.

Now for the conjecture...

"No matter what number you start with (step 1) you always end up with the 1,2,4 loop".

It's still just a conjecture because it has not been proven or unproven to date.

If you want to play around with this and see if you can prove or disprove it, be forewarned it has been proven true up to the number 2^68 so you'd have to start there if you wanted to use trial and error as has been done getting to that number.

Good luck if you do.

I thought this was interesting because it's such a simple problem but possibly not possible to prove or disprove.

As a side note, there is a scientist that is somewhat casually trying to show that the universe evolves from simple functions like this not from elementary particles. What is amazing about this function is it could generate huge structures before finally settling to that 1,2,4 sequence. if you pick a larger number something above 6000 you can get a wild variation, but even with smaller numbers like 27 you get 111 results before it settles to the 1,2,4 sequence which is still kind of lengthy.

Try it out it's kind of cool

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