My favorite series...

What comes next?
1
11
21
1211
111221
312211
...

Yes, I do like this one. Won't spoil it though.

and no cheating by looking it up in the encyclopedia of integer sequences...

Originally posted by forkedknight
What comes next?
1
11
21
1211
111221
312211
...

13112221
1113213211
31131211131221

????

Originally posted by forkedknight
and no cheating by looking it up in the encyclopedia of integer sequences...

Or at previous threads.

Originally posted by brobluto
13112221
1113213211
31131211131221

????

13211311123113112211
sorry disregard earlier version due to the fact that I can't count. 😛 I believe this version is right though

does the length of members of this series increase exponentially?

Once you determine what the rule entails, discovering the next term is very easy. Each number is determined exclusively by the previous number, by the way, but not in the standard mathematical way.

Originally posted by forkedknight
What comes next?
1
11
21
1211
111221
312211
...

Oh....

Got it... took a minute (or six) though.
😀

Originally posted by forkedknight
does the length of members of this series increase exponentially?

I think so, but I'm struggling with when the number 4 will occur in the series... (I don't think it will)

In order to get a 4, you would need either 1,2,or3 repeated 4 times:

1111
2222
3333

This would require a break from the sequence so I don't believe the number 4 is achievable. Is that correct?

Originally posted by brobluto
I think so, but I'm struggling with when the number 4 will occur in the series... (I don't think it will)

In order to get a 4, you would need either 1,2,or3 repeated 4 times:

1111
2222
3333

This would require a break from the sequence so I don't believe the number 4 is achievable. Is that correct?

I believe you are correct that the number 4 will never appear. since each 'description' is two digits long, and the second digit is the character that appeared, you will never have two descriptions in a row with the same second character.