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PostPosted: Mon Jun 03, 2002 1:54 am 
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Energizer Bunny
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1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 22, 23, 25, 28, 31, 34, 37, 43

these are ALL the positive numbers in the sequence. also, all negative numbers and 0 are also in the sequence. Note that this isn't really a 'sequence' so much as a set... there is no particular order to it, really.

The question is: How is the sequence generated?
Bonus question: what is the sequence called?

Vorn


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PostPosted: Mon Jun 03, 2002 1:59 pm 
*bump* this one isn't solved yet. so lets put it at the top of the list.


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PostPosted: Mon Jun 03, 2002 3:50 pm 
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Vorpal Bunny Slipper
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Just to clear it up, the missing numbers are:
6, 9, 12, 15, 18, 20, 21, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 40, 41, 42. It seems to exclude all the multiples of 3, from 6 to 42, and other numbers...

x3: 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42.


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PostPosted: Mon Jun 03, 2002 4:43 pm 
the others are...
20 26 29 32 38 40 41
2 2 5 - 2 13 - 29 - 2 2 2 2 2 - 2 19 - 2 2 2 5 - 41

So that's not it. lesse...

1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 22, 23, 25, 28, 31, 34, 37, 43
(1-5) 5, skip 1, (7-8 ) 2, skip 1, (10-11) 2, skip 1, (13-14) 2 , skip 1, (16-17) 2, skip 1, (19) 1, skip 2, (22-23) 2, skip 1, (25) 1, skip 2, (28 ) 1, skip 2, (31) 1, skip 2, (34) 1, skip 2, (37) 1, skip 5.
so, on non-skips, we have...
5 2 2 2 2 1 2 1 1 1 1 1
on skips we have...
1 1 1 1 1 2 1 2 2 2 2 5
these two are reversed. so i'd say that to make the sequence described,
We put infinity on either end of those sets, and 0 on the other end.
so there are 0 skipped below 1, and there are an infinite number skipped after 5. same for the inclusion list.
so, on non-skips, we have...
inf 5 2 2 2 2 1 2 1 1 1 1 1 0
on skips we have...
0 1 1 1 1 1 2 1 2 2 2 2 5 inf

Not sure what this sequence is called however.


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PostPosted: Mon Jun 03, 2002 6:36 pm 
20 26 29 32 35 38 40 41
A mildly corrected list.
the 35 has 5 and 7 as factors, if that helps fill anything in..


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PostPosted: Mon Jun 03, 2002 6:49 pm 
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Energizer Bunny
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Ok.

Jer is definitely on the right track.

Kaz is... not, despite having applied some strong sequence detecting algorithms to it.

While I'm at it, I'm removing 0 from the original sequence -- it seems to me, now, that it works better with it not in there. Besides, it makes the pattern stronger.

Hint time: The negative of the sequence is concerned with sums.

Vorn


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PostPosted: Mon Jun 03, 2002 7:10 pm 
Kazriko wrote:
20 26 29 32 35 38 40 41
A mildly corrected list.
the 35 has 5 and 7 as factors, if that helps fill anything in..


6, 9, 12, 15, 18, 20, 21, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 40, 41, 42.

now if we take 20, and go every 6 up from it, we get 26, 32, 38. leaving 29, 40, 41. other than 23, if we go every 3rd from 26 gives us the 29,32,35,38,41.

leaving the 40.
what if the 20 and 40 aren't part of the 3 pattern. Then it would be every 3rd starting from 6, and every third starting from 26. every 10th starting from 20? we also have to eliminate all the numbers above 43.
26 29 32 35 38 41 44 47 50 53 56 59
20 30 40 50 60
6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60
so, of the numbers above 43, this eliminates 44,45,47,48,50,51,53,54,56,57,59,60
leaving 46,49,52,55,58
gee, if we follow the pattern of the 6 and 26 ones, these can be eliminated with another sequence begining in 46, and eliminating every 3rd after that.
now lets put these patterns from 44 up...
44,47,50,53,56,59
45,48,51,54,57,60
46,49,52,55,58,61
these 3 patterns will kill anything else off above 43.

the 20,30,40 thing still doesn't make sense to me.


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PostPosted: Mon Jun 03, 2002 7:20 pm 
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Energizer Bunny
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10 is not involved.

20 is, though. And they ARE part of the 3 pattern -- kinda.


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PostPosted: Mon Jun 03, 2002 7:24 pm 
Hmm, if it's 20, plus every 20th after that (like Jeremiah said in channel), that would eliminate it, but this doesn't really fit in with the 3-patterns.....
:?


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PostPosted: Mon Jun 03, 2002 7:26 pm 
Vorn the Unspeakable wrote:
10 is not involved.

20 is, though. And they ARE part of the 3 pattern -- kinda.


The 3 patterns started at 6, 3 more than 3. So they did every third, leaving the first one out. If you wanted to do the same with 20, you would need to leave the 20 in. that's why i was thinking a 10 pattern, because the 10 is still there.


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PostPosted: Mon Jun 03, 2002 7:27 pm 
i guess the 3 patterns start at 20 point intervals however.


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PostPosted: Mon Jun 03, 2002 7:29 pm 
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Energizer Bunny
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Oh. 3 is also not directly involved.

Vorn


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PostPosted: Mon Jun 03, 2002 7:41 pm 
3 not involved huh? sigh... must be 6 patterns of 6 then.

6, 9, 12, 15, 18, 20, 21, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 40, 41, 42.

0 6 12 18 24 30 36 42 48 54
9 15 21 27 33 39 45 51 57
20 26 32 38 44 50 56
29 35 41 47 53 59
40 46 52 58
49 55

so, every 6th starting from 0,9,20,29,40,49 would give this pattern...

Ok, If this is wrong, i give. ;)
(this solution seems to be more of a group effort too..)


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PostPosted: Mon Jun 03, 2002 10:58 pm 
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Energizer Bunny
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You are mind-breakingly close. So close, in fact, that I think I'll give it to you now.

The negative of the set I described are McNugget Numbers, which can each be created by taking together whole boxes of Chicken McNuggets which come in packs of 6, 9, and 20.

http://mathworld.wolfram.com/McNuggetNumber.html

Vorn

(edit: stray tag)


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PostPosted: Tue Jun 04, 2002 2:18 am 
wow, even with knowing it's source, i don't know if i would have found it on my own. Makes sense in a computer science kind of way now, the sets i described, are formed by...
0 just 6 piecers
9 one 9 piece, then just 6 piecers
20 one 20, then just 6's
29 one 20, one 9, then just 6's
40 two 20's then 6's
49 two 20's, one 9, and then just 6's.

You never need more than 1 9 piece, because 2 of them can be formed by 3 6'ers, and never need more than 2 20's cause 3 20's can be formed by 10 6'ers.

that's a cool page. will have to bookmark it.

It's an interesting consequence that the skips/retains of the original set were mirrors of each other.
i'm sure someone has written a paper on that somewhere.


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PostPosted: Tue Jun 04, 2002 1:46 pm 
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Vorpal Bunny Slipper
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Point to Vorn, then, for making one we couldn't get. :)


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PostPosted: Tue Jun 04, 2002 3:27 pm 
yah, not without a lot of help did we even get close.

Of course, Jeremiah proved we could create really sadistic problems that can't be solved with the information given, so maybe a point for unsolvable problems is a bad idea. ;)

I could easily make a cryptogram with more than one charicter set, and more than one set of shifts, and a really wierd arrangement, and possibly nobody would ever solve it. does that mean I get a point? naa, i'd rather leave some hints in, and make it just convoluted enough to make it a challenge. That's what vorn's was. :)


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