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  What's the next number in the sequence  (Read 2303 times)
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Offline Riven
« League of Dukes »

JGO Overlord


Medals: 781
Projects: 4
Exp: 16 years


Hand over your head.


« Posted 2006-11-15 21:49:01 »

I was writing this LOD algorithm and found a certain sequence of values (by trial and error) for culling
the quads in the center, to make place for a higher LOD. Ofcourse the numbers became too hard to
narrow down in the following LODs, so I needed the formula!

So far for the introduction-story, which can be forgotten right away.


For this who like silly math assignments...


Give me the next 2 numbers of this sequence.

1  
2, 6, 26, 114, ..., ..., etc


It's a nasty one, and took me 15 minutes. Now I wonder what others come up with Smiley

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Offline zero

Junior Member





« Reply #1 - Posted 2006-11-15 22:49:56 »

one solution should be:

2^(2*n+1) - 2^(n+1) + 2   for n elem |N_0

sorry, I'm to lazy to put in n=4,5

took me also about 15min without a calculator (5 min for the formula and 10 min proof Undecided)

would have been faster but I thought of 2^prim(2+n) - .. because you sad it's a nasty one ;-)
Offline Riven
« League of Dukes »

JGO Overlord


Medals: 781
Projects: 4
Exp: 16 years


Hand over your head.


« Reply #2 - Posted 2006-11-15 23:20:30 »

I started with 1 instead of 0 (because of how the algorithm works).

1  
2  
|N_0 = 2^(2*n+1) - 2^(n+1) + 2
|N_1 = 2^(2*n-1) - 2^n + 2


Saves 1 addition Wink


I solved it during a chat-session about something else, got kinda hard to concentrate.

This is the first time I encountered a numeric-sequence that wasn't too obvious...


I hope it enjoyed your neurons a bit.

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Offline ChrisM

JGO Coder


Medals: 1
Projects: 1


END OF LINE.


« Reply #3 - Posted 2006-11-15 23:51:57 »

OUCH!  Just stubbed my brain....

-Chris

Offline tusaki

Junior Member


Medals: 1


In a mad world only the mad are sane.


« Reply #4 - Posted 2006-11-16 00:16:01 »

that's a nice formula.

now I want an explanation how it works Grin
Offline Riven
« League of Dukes »

JGO Overlord


Medals: 781
Projects: 4
Exp: 16 years


Hand over your head.


« Reply #5 - Posted 2006-11-16 00:35:32 »

Well.... if I'd say that it's top-secret, I'd lie.

Consider a grid of cells,
with inside it, another grid of smaller cells,
with inside it, another grid of smaller cells,
with inside it, another grid of smaller cells,
etc.

Which 'center cells' inside the LOD should be culled to prevent overlap?
That's what this formula calculates.

BTW, the placement of the lower LOD-grids, is corrected (snapped) by:

1  
2  
3  
4  
5  
6  
7  
8  
for (int lod = 0; lod < lods; lod++)
{
   for (int k = 0; k <= lods; k++)
   {
      x -= (((xCameraTile >> k) & 1)) << k;
      z -= (((zCameraTile >> k) & 1)) << k;
   }
}


If there would be a direct formula for that one... I'd be thrilled, but I wouldn't really need it Smiley


I create this kind of black-magic code (for me at least) by writing out the LOD-math for a few levels,
then searching for patterns, transforming it into formulas, where the formula's don't make much
sense to me, to be honest. In the documentation I write how I created them.

I just don't have the time to examin what really happens. Not really interested either Tongue

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Offline Falken

Senior Newbie




biggidy bong


« Reply #6 - Posted 2006-11-16 00:42:33 »

Great. Now for your next challenge.
Could you tell me the next 7 numbers in this sequence... http://www.lottery.co.uk/euro-millions.htm  Cheesy
Offline Riven
« League of Dukes »

JGO Overlord


Medals: 781
Projects: 4
Exp: 16 years


Hand over your head.


« Reply #7 - Posted 2006-11-16 00:44:30 »

4, 8, 15, 16, 23, 42 and the age of your imaginairy friend.

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Offline Falken

Senior Newbie




biggidy bong


« Reply #8 - Posted 2006-11-16 01:05:43 »

LOL. Thanks.  If I win, you can have my Oceanic flight tickets to Los Angeles. Grin
Offline darkprophet

Senior Member




Go Go Gadget Arms


« Reply #9 - Posted 2006-11-16 01:51:33 »

Oh god...not Lost! Its haunting me to this day...

* darkprophet closes ears and runs shouting BLAH BLAH BLAH BLAH BLAH BLAH BLAH

Friends don't let friends make MMORPGs.

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