Pattern

[BicycleTree]

0, 1
0, 2, 3, 1
0, 4, 6, 2, 3, 7, 5, 1
?

What line comes next in the sequence?

[<<<GUILLE>>>]

0, 1
0, 2, 3, 1
0, 4, 6, 2, 3, 7, 5, 1
?

What line comes next in the sequence?

0, 6, 12, 4, 6, 14, 10, 1, amd three more numbers I haven't manage to get. I know that each number is twice as much as the one on top, and that each line has twice as much more new as the line on top had new.

[SplinterIon]

Guille - Wouldn't that be
0, 8, 12, 4, 6, 10, 2, s, t, u, v, w, x, y, z, 1
If I were to follow your doubling pattern.

[quark]

0,8,12,4,6,14,10,2,3,11,9,1,?,?,?,? :uhh:

[<<<GUILLE>>>]

Guille - Wouldn't that be
0, 8, 12, 4, 6, 10, 2, s, t, u, v, w, x, y, z, 1
If I were to follow your doubling pattern.

o, yes: I didn't center in the post while I wrote it.

thanks SplinterIon.

[AntonVrba]

How about?

0,2,3,1 _/\_ 1+2=3
0, 4, 6, 2, 3, 7, 5, 1 _/\_1+4 = 5 is followed by
0, 8,12, 4, 6, 14, 10, 2, 3 49,41, 33, 25, 17, 9, 1 _/\_ 1+8=9

I think it fits.

[<<<GUILLE>>>]

How about?

0,2,3,1 _/\_ 1+2=3
0, 4, 6, 2, 3, 7, 5, 1 _/\_1+4 = 5 is followed by
0, 8,12, 4, 6, 14, 10, 2, 3 49,41, 33, 25, 17, 9, 1 _/\_ 1+8=9

I think it fits.

Whats that _/\_ sign?

I just noticed that the sum the number 2,4,8,16.. double each time plus the last number of the sequence always equals the second last number of the same horizontal line.

[AntonVrba]

[QUOTE=<<<GUILLE>>>]Whats that _/\_ sign?
QUOTE]
_/\_ hmmmm a thingimagic :smile: , or a bracket broken in two or a volcano or whatever you want it to be, I ment it to be a end of line and then added some remarks.

[Zygotic Embryo]

how in god's name did you come up with that.

lol, make's me feel stupid.

[ArielGenesis]

bicycletree, are you still there ???

[ArielGenesis]

0,8,12,4,6,14,10,2,3,11,9,1

hey quark, how come you can come up with the last 4 number

[ArielGenesis]

0, 1
0, 2, 3, 1
0, 4, 6, 2, 3, 7, 5, 1
0, 8, 12, 4, 6, 14, 10, 2, 3, 11, 15, 7, 5, 13, 9, 1

my friend told me of this

[quark]

That makes sense. I knew I was missing the difference of 4 between 2nd and 4th digits but overlooked the +4 and -4 alternate cycle. Nevertheless, I strongly doubt the construction of this series further. No rule is applicable for finding the first of the four digits, IMHO. Perhaps, the OP can throw some light.

[BicycleTree]

0, 1
0, 2, 3, 1
0, 4, 6, 2, 3, 7, 5, 1
0, 8, 12, 4, 6, 14, 10, 2, 3, 11, 15, 7, 5, 13, 9, 1

my friend told me of this
You got it Ariel. You want to explain the pattern?

There's something special about this pattern, when each of the numbers in a line is written in binary.

[cdhotfire]

Please, tell the how you got this awnser, i might have to pull all my hair off. :rolleyes:

[quark]

I know that the difference between 1st, 2nd and 3rd, 4th numbers is +2 and -2 respectively; difference between 2nd and 3rd numbers is 2 for second row. For second row it is +4, -4 and 2 and so on. So for forth row it should give +8,-8 and 4. So the numbers just double. But the trouble is the starting number of new 4 number set. Once we get it, rest of the 3 numbers can be constructed using the above logic. Should it always be 3? Did it with 4 bit binary. The binary digit 1 seems to be shifting left.

[ArielGenesis]

0,1
at first we multiply them by two as what discuss earlier
0,2
and then we mirror the number
0,2,2,0
then we add the number that we just aded by 1
0,2,3,1

i dont know how but my friend, she just look at it and figure it out in a minute

[BicycleTree]

Yep, that's how it's made.

The special thing is that it's a Gray code. If you write the numbers in one of those sequences in binary (with a uniform number of digits) it cycles through all the numbers say 0-7 so that at each step only one binary digit changes.

[Rahmuss]

I thought I was on to something and got

0,8,12,4,6,14,10,2,3,11,15,7,17,13,5,1

I got that by doubling the line before and then adding 3 to the 1st #, 2nd #, 3rd # (skip middle number 4th # in this case) add 3 to 5th #, 6th # 7th # and then put 1 on the end.

A little too complicated; but it works for that second and third stage.

[gonpost]

*oops* was already here...cool one though.