Binary Sequence: What Comes Next?

In summary: DIn summary, this person discovered a sequence of binary digits that can be passed into another binary digit. They are not sure if this is a joke, but anyone could take a # as 197847389748838393384848484949393822636464785885984 and pass it into base 2.
  • #1
Moo Of Doom
366
1
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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  • #2
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"
 
  • #3
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
 
  • #4
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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  • #5
Is that really 00 at the end and not 01?
 
  • #6
BicycleTree said:
Is that really 00 at the end and not 01?

Yes. That should be a clue.
 
  • #7
Well, if you chop off the last 0 it's a palindrome.
 
  • #8
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.
 
  • #9
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.

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.
 

Related to Binary Sequence: What Comes Next?

1. What is a binary sequence?

A binary sequence is a sequence of 0s and 1s, also known as bits, used to represent information in computers. It is a fundamental concept in computer science and is used in various applications such as coding, data compression, and cryptography.

2. How do you determine what comes next in a binary sequence?

The next number in a binary sequence is determined by following a specific pattern. The pattern depends on the type of binary sequence, such as arithmetic, geometric, or random. For example, in an arithmetic sequence, the difference between each consecutive number is constant. In a geometric sequence, each number is multiplied by a constant factor to get the next number.

3. What are some real-life applications of binary sequences?

Binary sequences have various applications in the real world. It is used in computer programming to represent data and instructions, in telecommunication to transmit and receive data, in digital electronics to control the flow of electricity, and in genetics to represent DNA sequences.

4. Can binary sequences be infinite?

Yes, binary sequences can be infinite. Just like any other sequence, it can continue indefinitely. However, in practical applications, binary sequences are usually finite and have a specific purpose or pattern.

5. Is there a limit to the complexity of binary sequences?

No, there is no limit to the complexity of binary sequences. With a combination of 0s and 1s, an infinite number of patterns and sequences can be created. As technology advances, more complex and longer binary sequences are being used in various applications.

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