# Pattern sequence brain teaser

1. Mar 21, 2005

### ArielGenesis

1
11
21
1211
111221
312211
13112221
...

2. Mar 21, 2005

### gerben

1113213211
31131211131221
...

3. Mar 22, 2005

### ArielGenesis

nice ;), you have meet those i guess.

4. Mar 22, 2005

### 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

5. Mar 22, 2005

### 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!)

Last edited: Mar 22, 2005
6. Mar 22, 2005

### 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'.

7. Mar 23, 2005

### mapper

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

8. Mar 23, 2005

### K.J.Healey

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)

9. Mar 24, 2005

### ArielGenesis

1
11
21
1211
111221
312211
13112221

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