What is the pattern sequence for this brain teaser?

[ArielGenesis]

1
11
21
1211
111221
312211
13112221
...

Please continue...

 

[gerben]

1113213211
31131211131221
...

 

[ArielGenesis]

nice ;), you have meet those i guess.

 

[TenaliRaman]

For general information,
these sequences are called conway sequence also known as look and say sequence
http://mathworld.wolfram.com/LookandSaySequence.html

It is known that this sequence has many properties related to discrete maths, combinatorics and graph theory but the paper which discusses these things is not available for free :(.

-- AI

 

[DaveC426913]

Unless I'm wrong, this sequence will never contain any number larger than 3, correct?

You will never have ...211113..., because that's really ...3113...

Edit: Ah yes. Upon further reading, I see my observation is corroborated. (Good to know!)

 

[DaveC426913]

Can someone explain this, or at least give an example:

"In fact, the constant is even more general than this, applying to all starting sequences (i.e., even those starting with arbitrary starting digits), with the exception of 22, a result which follows from the cosmological theorem. Conway discovered that strings sometimes factor as a concatenation of two strings whose descendants never interfere with one another. A string with no nontrivial splittings is called an "element," and other strings are called "compounds." It is postulated that every string of 1s, 2s, and 3s that does not contain four of the same number in succession eventually "decays" into a compound of 92 special elements, named after the chemical elements."

It seems to come down to the 'factoring', which they call 'decaying'.

 

[mapper]

wouldve been harder if it were:
1
11
...
continue.

 

[K.J.Healey]

wouldve been harder if it were:
1
11
...
continue.

if by harder you mean less specific then yes.

1
11
111
1111
11111

is one solution

1
11
101
111
1001
1011
1101
1111
...
is another

so is
1
11
31
57
83
...

and one more
1
11
121
1331
14641
...

What are they all? (that i wrote)

 

[ArielGenesis]

1
11
21
1211
111221
312211
13112221

i use this as i think that number 3 must come at least twice for anyone to get the pattern