What line comes next in the sequence?

In summary, Guille observed that the numbers in a sequence double each time, and when the last number of the sequence is reached, the second-to-last number of the sequence is also reached.
  • #1
BicycleTree
520
0
0, 1
0, 2, 3, 1
0, 4, 6, 2, 3, 7, 5, 1
?

What line comes next in the sequence?
 
Physics news on Phys.org
  • #2
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.
 
  • #3
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.
 
  • #4
0,8,12,4,6,14,10,2,3,11,9,1,?,?,?,? :uhh:
 
  • #5
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.
 
  • #6
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:
  • #7
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.
 
  • #8
<<<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.
 
  • #9
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:

1. What is the pattern or rule behind the sequence?

The first step in determining the next line in a sequence is to identify the underlying pattern or rule. This can be done by looking for a consistent increase or decrease in numbers, letters, or symbols. It can also involve identifying relationships between elements in the sequence, such as doubling or adding/subtracting a constant value.

2. How do I use the pattern to predict the next line?

Once the pattern or rule has been identified, it can be used to make a prediction about the next line in the sequence. This can be done by applying the pattern to the last known element in the sequence, or by using a formula or equation to calculate the next value.

3. What if there are multiple possible patterns for the sequence?

In some cases, there may be more than one possible pattern or rule for a sequence. If this is the case, it is important to consider all possibilities and see which one best fits the given sequence. This may involve trying out different patterns and seeing if they produce the same result for the given sequence.

4. Are there any tricks or shortcuts for solving these types of problems?

While there is no one foolproof method for solving sequence problems, there are some tips and tricks that can make the process easier. These include looking for common patterns, breaking the sequence into smaller parts, and using the process of elimination to rule out incorrect patterns.

5. How can I practice and improve my skills in solving sequence problems?

The best way to improve in solving sequence problems is through practice. There are plenty of online resources and books that offer practice problems and solutions, as well as tips and strategies for solving them. Additionally, regularly engaging in activities such as puzzles and brain teasers can also help improve pattern recognition and problem-solving skills.

Similar threads

Replies
3
Views
458
  • Calculus and Beyond Homework Help
Replies
1
Views
225
  • Precalculus Mathematics Homework Help
Replies
5
Views
920
Replies
1
Views
1K
  • Programming and Computer Science
Replies
4
Views
3K
  • Precalculus Mathematics Homework Help
Replies
11
Views
725
  • Biology and Medical
Replies
1
Views
955
Replies
1
Views
945
  • Precalculus Mathematics Homework Help
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
360
Back
Top