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10 replies to this topic

#1 unreality

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Posted 06 March 2008 - 10:34 PM

Probably many of you have heard of the infamous and unsolved 3x+1 problem. Many others have not, I'm sure.

Here it is, in my words:

*****

Take any integer greater than zero. Call this number x.

If it is even, halve it. In other words, x becomes x/2
If it is odd, x becomes 3x+1

The sequence, for all numbers tested so far, ends up in the endlessly repeating loop of 4,2,1,4,2,1,4,2,1...

While many numbers have been tested by computers, this doesn't prove or disprove the conjecture that the sequence will fall into this loop. Can you provide a counterexample (it would have to be BIG), or give a proof as to why it always iterates to 1, or a proof why it sometimes doesn't? Will you be the first?

Spoiler for a few things of note...


Just curious to see what you guys find. :P
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#2 EventHorizon

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Posted 06 March 2008 - 10:44 PM

The Collatz conjecture (also known as Ulam's problem)

ummm.....nope...no answer off the top of my head....but if someone here solves it....I'd love to be a coauthor on the paper ;)
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#3 Lost in space

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Posted 06 March 2008 - 11:19 PM

We need some help on this one
Largis
Wiles
Feramt
Pythagaros
Luck
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#4 unreality

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Posted 07 March 2008 - 02:03 AM

You mispelled some of those:

Feramt should be Fermat
Pythagaros should be Pythagoras
Wiles should be Willes (I think)

anyway, yeah. I would also like to be a coauthor ;D lol. I was thinking we could discuss it or something. I dunno. Somebody will be the first to solve it, if it's solvable :P which I hope it is
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#5 the new riddler

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Posted 07 March 2008 - 02:08 AM

You mispelled some of those:

Feramt should be Fermat
Pythagaros should be Pythagoras
Wiles should be Willes (I think)

anyway, yeah. I would also like to be a coauthor ;D lol. I was thinking we could discuss it or something. I dunno. Somebody will be the first to solve it, if it's solvable :P which I hope it is


shouldn't it end up as only 1 or 2, because 4/2 is 2...
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#6 unreality

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Posted 07 March 2008 - 02:32 AM

Yeah, it's about PROVING or DISPROVING that it will ALWAYS end in the sequence 4,2,1,4,2,1,4,2,1...(etc)
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#7 storm

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Posted 07 March 2008 - 02:46 AM

My my...I can do another Journal paper on this......
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#8 Lost in space

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Posted 07 March 2008 - 08:48 AM

You mispelled some of those:

Feramt should be Fermat
Pythagaros should be Pythagoras
Wiles should be Willes (I think)

anyway, yeah. I would also like to be a coauthor ;D lol. I was thinking we could discuss it or something. I dunno. Somebody will be the first to solve it, if it's solvable :P which I hope it is


Probably true am digitaly dyslexic when i'm tired am ko this mroning htough!

Good luck with it!
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#9 ent474

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Posted 07 March 2008 - 06:21 PM

2 (1) 3(10)... it's totally not hte same :D

i wonder how many children are on this site.

1 (me)... <_<
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#10 statman

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Posted 07 March 2008 - 09:08 PM

Another question I would have...how fast does a number reach the repeating sequence?
10-5-16-8-4-2-1-4-2-1
11-34-17-52-26-13-40-20-10-5-16-8-4-2-1-4-2-1
12-6-3-10-5-16-8-4-2-1-4-2-1
13-40-20-10-5-16-8-4-2-1-4-2-1
14-7-22-11-34-17-52-26-13-40-20-10-5-16-8-4-2-1-4-2-1

is there a relationship between the starting x value and the length of the sequence?
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