What line comes next in the sequence?

  • Context: High School 
  • Thread starter Thread starter BicycleTree
  • Start date Start date
  • Tags Tags
    Line Sequence
Click For Summary

Discussion Overview

The discussion revolves around identifying the next line in a numerical sequence, with participants exploring various patterns and rules governing the sequence. The scope includes mathematical reasoning and speculative approaches to sequence generation.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Some participants suggest that each number in the sequence is derived by doubling the previous line's numbers and adding specific values.
  • Others propose that the sequence follows a pattern involving alternating additions and subtractions, with some participants noting a difference of 4 between certain digits.
  • A participant mentions a potential connection to Gray code, where only one binary digit changes at each step.
  • Some participants express uncertainty about the rules for generating the first of the new numbers in the sequence, indicating a lack of clarity on how to extend the pattern.
  • One participant describes a method involving mirroring numbers and adding one, though they express confusion about the logic behind it.
  • Another participant presents a sequence they derived by doubling previous numbers and adding specific values, but acknowledges it may be overly complicated.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the rules governing the sequence, with multiple competing views and methods proposed for generating the next line. The discussion remains unresolved regarding the correct approach to extend the sequence.

Contextual Notes

Some participants note missing assumptions and the complexity of determining the starting number for new sets in the sequence. There are also references to binary representations and their implications for the sequence structure.

BicycleTree
Messages
519
Reaction score
0
0, 1
0, 2, 3, 1
0, 4, 6, 2, 3, 7, 5, 1
?

What line comes next in the sequence?
 
Mathematics news on Phys.org
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:

Similar threads

MHB (Seemingly) Random Sequences
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad What is the missing number in this number sequence pattern?
  • · Replies 3 ·
Replies
3
Views
4K
High School Weird stuff on infinite numerical sequences in a Soviet book
  • · Replies 5 ·
Replies
5
Views
1K
High School Golden Ratio in Collatz-like sequences
  • · Replies 1 ·
Replies
1
Views
2K
High School Recursive sequences - notation question
  • · Replies 11 ·
Replies
11
Views
2K
High School Arithmetic and our place value system
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Is this Recursive Pattern in the Collatz Sequence Known?
  • · Replies 3 ·
Replies
3
Views
2K
High School What is the formula for this sequence for n-th number
  • · Replies 5 ·
Replies
5
Views
2K
High School About a definition: What is the number of terms of a polynomial P(x)?
  • · Replies 48 ·
2
Replies
48
Views
6K
Undergrad Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
  • · Replies 16 ·
Replies
16
Views
3K