Binary Sequence: What Comes Next?

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    Binary Sequence
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Discussion Overview

The discussion revolves around a binary sequence presented by a participant, with others attempting to determine the next term in the sequence. Participants explore various interpretations, patterns, and potential rules governing the sequence, engaging in a mix of exploratory reasoning and technical analysis.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents a binary sequence and asks what comes next, suggesting uncertainty about its nature.
  • Another participant proposes that the next term should be "01," based on their interpretation of the sequence.
  • A different participant guesses that the next term is a "0," noting a pattern of "1 followed by 0."
  • Further terms are provided by the original poster, indicating a more complex structure than initially perceived.
  • Some participants question whether the last term is "00" or "01," indicating a potential misunderstanding of the sequence's structure.
  • Hints are provided regarding the relationship between the revealed terms and the sequence's construction, suggesting a connection to the number of terms presented.
  • Another participant suggests that the sequence can be viewed as a palindrome if the last "0" is removed.
  • Multiple participants propose different interpretations of how to associate blocks of the sequence with binary digits, leading to various generated patterns.
  • One participant acknowledges that their interpretation differs from the original poster's intent but still produces a valid sequence.

Areas of Agreement / Disagreement

Participants express differing views on the correct interpretation of the sequence and the next term. There is no consensus on a single correct answer, and multiple competing interpretations remain throughout the discussion.

Contextual Notes

Some participants note the potential for different interpretations based on how terms are grouped or associated, indicating that the sequence's structure may depend on specific definitions or assumptions that are not fully resolved.

Who May Find This Useful

Readers interested in binary sequences, pattern recognition, and combinatorial reasoning may find the discussion relevant to their interests.

Moo Of Doom
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Not sure if this has been done... I sort of discovered this sequence myself, but who knows...

01000101010001000100010101000101...

What comes next?
 
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I hope this isn't a joke.Anyone could take a # as 197847389748838393384848484949393822636464785885984 and pass it into base 2

Daniel.

On normal basis,it should be "01"
 
I don't know, but here's my answer: Since every 1 is followed by a 0 in the pattern so far, I'm going to guess that the next item in the sequence is a 0[/color]
 
You're both correct as to the terms, but have not found out the pattern...

I'll post some more terms, though.

0100010101000100010001010100010101000101010001000100010101000100

That should be a big help.

P.S. This is in no way a joke. (And it has only to do with "binary" in the sense of needing two symbols)

EDIT: This includes the original terms.

EDIT 2: It seems to be showing a space in the terms... there shouldn't be one...
 
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Is that really 00 at the end and not 01?
 
BicycleTree said:
Is that really 00 at the end and not 01?

Yes. That should be a clue.
 
Well, if you chop off the last 0 it's a palindrome.
 
Here's a hint: Consider the number of terms I revealed the first post and the second post.[In White]

And Bicycle Tree: I totally didn't even notice that. Cool.
 
The last 0 should totally be a 1.
 
  • #10
BicycleTree said:
The last 0 should totally be a 1.

Hint: That's pretty much the idea behind the sequence.

That and my previous one should probably be enough, but I can keep trying. Tell me if you really want the answer.
 
  • #11
I don't know, what's the answer? There are some repetitive patterns and they all predict a final 1.
 
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  • #12
EDIT: Answer removed in order to give other people a chance. Hints still apply.
 
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  • #13
That's pretty good.
 
  • #14
Thanks. Glad it was challenging. :biggrin:
 
  • #15
How about this sequence, then?

01101001100101101001011001101001...
 
  • #16
Answer:Associate the block 0110 with 0 and 1001 with 1. The sequence starts with 0110 and the n'th block of 4 thereafter is determined by the n'th entry in the pattern. For example, the fourth block of 4 is determined by the 4th entry, namely 0, so it is 0110.[/color]

That one was much easier, took only a minute or two.
 
  • #17
Well, I don't know why that one was so easy and the other one wasn't because I just tried the same idea on the first one and got this: 01 associates with 0, 00 associates with 1, start with 01 and proceed as in the post above, and that generates the original pattern you posted.
 
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  • #18
Wow. That works indeed, but is not my original thinking. Good job, BicycleTree!

My Answer:

Instead of changing the last letter of the previous sequence, just write the opposite of the previous sequence by changing all the 0s to 1s and the 1s to 0s:

0->1
01->10
0110->1001
01101001->10010110
etc.

Can you prove your version is equivalent to my version? :)

EDIT: By the way, for both of those sequences (or any like it), associating any group of 2^n terms with the digits of the sequence will result in the same sequence :)
 
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  • #19
EDIT: By the way, for both of those sequences (or any like it), associating any group of 2^n terms with the digits of the sequence will result in the same sequence :)
Yeah, I figured that. Might be able to use that to prove it, though you'd have to prove that property first. Not trying it though right now.
 

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