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[sudgy]

Well, if the conjecture is true, the sequence will always have numbers.  If it isn't true, at some point one of the numbers in the sequence would be equal to Infinity.  I would think that finding a pattern in the numbers would show that the sequence will never have Infinity as an entry, and it would mean that it's true.

[Tables]

Hm, I think you have to be careful with that. For example, take the sequence generated by the formula 1/(x-20,000). Clearly this will have a pattern and obviously, a defining formula - but it fails/isn't defined/is infinite at 20,000. Now while we can see that clearly happens in this formula, but it could well be the case that the formula defining the pattern you're generating there is complex enough that working out if it's undefined/infinite at some points might be just as hard as solving the Collatz Conjecture itself.

Of course, if your formula can be generated by an equation of some form which can be proven to always output integers (or numbers, possibly, depending on what's necessary), then it works. But you can't assume that will happen.

Edit: Let's fix my formula since I derped.

[sudgy]

And, that's why I didn't want to say why it was in the first place because now everybody gives up...

Also, FYI, the formula you said is undefined until it hits the square root of 20,000.

[scott_pilgrim]

I wasn't wanting to say too much about it because the people who knew what it was would just find it preposterous to look for a pattern, but oh well.

And, that's why I didn't want to say why it was in the first place because now everybody gives up...

It's normal for people with mathematical minds to pretend from time to time that the simple, unsolved problems of mathematics are within their grasp.  If enough people keep pretending that, those problems won't stay unsolved forever.

If you remind me in ~a week and a half when I am no longer panicking over my thesis, I may look through/run tests on the numbers more carefully and see if I can find anything.

[heron]

Well, even sudgy doesn't expect their to be a pattern. He posted it in random stuff after all.

[sudgy]

I wasn't wanting to say too much about it because the people who knew what it was would just find it preposterous to look for a pattern, but oh well.

And, that's why I didn't want to say why it was in the first place because now everybody gives up...

It's normal for people with mathematical minds to pretend from time to time that the simple, unsolved problems of mathematics are within their grasp.  If enough people keep pretending that, those problems won't stay unsolved forever.

I was just doing a whole bunch of random stuff and saw how much organization there was with that list, and was curious if there was a pattern.

[WalrusMcFishSr]

How exactly did you generate that sequence sudgy? It might be helpful to know, as much fun as it is to play numerical Zendo haha

[sudgy]

This is the number of iterations (I think that's a correct usage of the word?) needed for each of these numbers to reach one:

1: 1
2: 2
3: 8
4: 3
5: 6
6: 9
7: 17
8: 4
9: 20
10: 7
11: 15
12: 10
13: 10
14: 18
15: 18
...

If all odd numbers reach one, all even ones do too.  If we have a large list of what we know reaches one, all the even numbers up to twice as big as the highest number we know also reach one.  So if we can find a pattern in how much difference there is from an even number to the next odd number, that means we can keep using that to get all natural numbers.  The difference from each even number to the next odd number is this:

(actually, now I see why my program left out the one, I was thinking you should 1->2 also )

8 - 2 = 6
6 - 3 = 3
17 - 9 = 8
20 - 4 = 16
15 - 7 = 8
10 - 10 = 0
18 - 18 = 0
...

And that's the sequence.

[qmech]

On the topic of xkcd and games (especially cookie clicker): http://castle.chirpingmustard.com

I'm not entirely sure what's happening yet, but this is brilliant:

Math.ceil(Math.PI) castles
196 sand of 377 needed
0 sand/mNP

[Tables]

I still don't understand what your sequence is doing... in particular can you clarify this?

"So if we can find a pattern in how much difference there is from an even number to the next odd number, that means we can keep using that to get all natural numbers.  The difference from each even number to the next odd number is this"

[Kirian]

I still don't understand what your sequence is doing... in particular can you clarify this?

"So if we can find a pattern in how much difference there is from an even number to the next odd number, that means we can keep using that to get all natural numbers.  The difference from each even number to the next odd number is this"

I think what he's saying is that the proposition "it is possible to predict the next number in this sequence" is equivalent to the Collatz conjecture.

[sudgy]

Say we know that these numbers reach one (which we do):

1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Now, obviously, double all these numbers reach one two, so we know:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20 (and more doubles)

If we can figure out a way to find out how the next odd number reaches one (through iterations), then we can fill in the odd numbers:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

Now we can double these...etc.

There could be easier ways, but that sequence that I made just looks so uniform that I feel it has to have something...

I still don't understand what your sequence is doing... in particular can you clarify this?

"So if we can find a pattern in how much difference there is from an even number to the next odd number, that means we can keep using that to get all natural numbers.  The difference from each even number to the next odd number is this"

The first sentence I just explained earlier in this post, and the second sentence is leading up to the sequence which I say right afterwards.

[Thisisnotasmile]

There could be easier ways, but that sequence that I made just looks so uniform that I feel it has to have something...

The frequency of digits in pi are pretty uniform after you go so far, but that doesn't mean there's a pattern.

[WalrusMcFishSr]

I know Cookie Clicker is totes passe by now, but I left it running all week, and upon my return just now, I popped my wrinklers for 250 quadrillion* EACH. Dwarfed by some of your empires no doubt but it sure felt good.



*250 billiard in Ozle units

[Archetype]

I've finally figured out how to use Inspect Element and I'm having way too much fun with it.

[WalrusMcFishSr]

Here's a crazy function. It's defined for these values:

f(0) = 6
f(1) = 2
f(2) = 5
f(3) = 5
f(4) = 4
f(5) = 5
f(6) = 6
f(7) = 3
f( = 7
f(9) = 6

What's up with this cah-razy function?

Here's another one in a similar vein. It is well-defined for numbers from 1 to at least 89.

g(1) = 1
g(2) = 2
g(3) = 3
g(4) = 3
g(5) = 2
g(6) = 3
g(7) = 4
g( = 5
g(9) = 3
g(10) = 2
g(11) = 3
g(12) = 4
g(13) = 5
g(14) = 5
g(15) = 4
g(16) = 5
g(17) = 6
g(18) = 7
g(19) = 5
g(20) = 4
g(21) = 5
g(22) = 6
g(23) = 7
g(24) = 7
g(25) = 6
g(26) = 7
g(27) = 8
g(28) = 9
g(29) = 7
g(30) = 6
g(31) = 7
g(32) = 8
g(33) = 9
g(34) = 9
g(35) = 8
g(36) = 9
g(37) = 10
g(38) = 11
g(39) = 9
g(40) = 4
g(41) = 5
g(42) = 6
g(43) = 7
g(44) = 7
g(45) = 6
g(46) = 7
g(47) = 8
g(48) = 9
g(49) = 7
g(50) = 2
...

[WalrusMcFishSr]

That's not an error. Cool smileys are part of the domain.

[qmech]

Cool smileys have certainly been part of the domain of discourse.

[SirPeebles]

That's not an error. Cool smileys are part of the domain.

He's the shaded portion of the domain.

[SirPeebles]

Finally hit 1 trillion cookies per second, although I already had the achievement from the olden days when Elder Frenzy triggered it.

Just hit 2 trillion cookies per second.  I started playing on October 13, so my first trillion took 29 days, and my second trillion took 21 days.

[AHoppy]

As of today: I have a handlebar moustache

[SirPeebles]

As of today: I have a handlebar moustache

Shave off your no-shave November beard?

[AHoppy]

As of today: I have a handlebar moustache

Shave off your no-shave November beard?

Well, I started back in October, so it had been going for 2 months.  But basically yes

[eHalcyon]

[liopoil]

seems like this thread just keeps coming back to fractals