What line comes next in the sequence?

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The discussion revolves around identifying the next line in a numerical sequence, with participants analyzing patterns in the sequences provided. The sequences start with simple numbers and evolve into more complex patterns, with participants suggesting that the numbers double or follow specific arithmetic rules. A notable observation is the connection to binary representation and Gray code, where only one bit changes at a time. Participants explore various methods to derive the next numbers, including doubling previous values and applying alternating addition and subtraction patterns. There is a consensus that while some rules can be applied to find subsequent numbers, the starting point for new sets remains ambiguous. The conversation highlights the challenge of deciphering the underlying logic of the sequences, with some contributors expressing frustration and others sharing insights into the mathematical relationships at play.
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0, 1
0, 2, 3, 1
0, 4, 6, 2, 3, 7, 5, 1
?

What line comes next in the sequence?
 
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BicycleTree said:
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.
 
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.
 
0,8,12,4,6,14,10,2,3,11,9,1,?,?,?,? :rolleyes:
 
SplinterIon said:
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.
 
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.
 
Last edited:
AntonVrba said:
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.
 
<<<GUILLE>>> said:
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.
 
how in god's name did you come up with that.

lol, make's me feel stupid.
 
  • #10
bicycletree, are you still there ?
 
  • #11
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
 
  • #12
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
 
  • #13
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.
 
  • #14
ArielGenesis said:
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.
 
  • #15
Please, tell the how you got this awnser, i might have to pull all my hair off. :rolleyes:
 
  • #16
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.
 
  • #17
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 don't know how but my friend, she just look at it and figure it out in a minute
 
  • #18
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.
 
  • #19
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.
 
  • #20
*oops* was already here...cool one though.
 
Last edited:

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