11
221
31132
412211143
51322111231112154
614231113321211222112411111312165
71524111433121311232113421222111112113221223112511111211141213176
816251115341214112421144313122311111311332213212331135212111212321111221121121142222111122132312241126111111131112121115121413187


What's the next line in this sequence?

um, are those supposed to be numbers, as in, eleven, two hundred twenty one, etc, or 1 1 2 2 1 3 1 1 3 2 or a mix? if it's a mix, mind putting spaces in between the numbers? then I can give you an answer very easily

would like to see someone explain the pattern, been trying to find it also but btw, is there a specific method for finding the next number in a sequence like that or is it just feeling?

So far I figured the next line will have 257 terms and it's first few should be 917651116351215 while last two should be 98.

Anyone knows the logic?
This started to bug me.

the amount of additional numbers is always a power of 2. In this case 2^7 = 128, leaving us with 257 terms total
First number counts upwards: 9
Last 2 numbers each count upwards: 98

in between these it alternates between lines that are counting upwards and a different sequence
The counting upwards parts go something like 8 6 5 5 4 4 4 4 so that sequence probably continues with 8 3s and then 16 2s etc.
The sequences seperating these from each other goes something like 1 2 111 3 121 112 211
After that it gets kind of weird and im losing the pattern, which might have something to do with the ending pattern being longern and the 2nd to last line changing from the start block pattern to the end block pattern, which makes comparing the 2 last patterns to each other more difficult.
The gist of this divider sequence seems to be playing through different possible combinations of numbers that add up to a total sum of X. After going through these, you continue you X+1 as your next sequence. Though im not sure yet why not all of the possible combinations are used and in which order they are used.
1 is the only way to write out 1.
2 adds up to 2, but 11 is not being used here
111 and 3 both add up to 3, but 12 and 21 are not being used.
121, 112 and 211 all equal 4 and i think the sequence continues with 4 --> 31 --> 122 (first 5) --> 11111

yeah there is the interesting property that in the first line there are only 1's
in the second line there are 1's and 2's
in the third line there are 1's, 2's, and 3's (and so on)....
not sure what this means...

1+1 = 2 = 2^1 + 0
2+2+1 = 5 = 2^2 + 1
3+1+1+3+2 = 10 = 2^3 + 2
4+1+2+2+1+1+1+4+3 = 19 = 2^4 + 3
5+1+3+2+2+1+1+1+2+3+1+1+1+2+1+5+4 = 36 = 2^5 + 4

so the sum of each line is 2^n + n - 1 (where n is the line number)

of course this does not tell us the next sequence exactly (it only describes its sum), next we need to figure out how the digits are chosen to create that sum.

for example, the 3rd line could have been written:
3+3+3+1 = 10
so the question is, why was it written as:
3+1+1+3+2 = 10

This post was edited by Azrad on Apr 24 2013 07:38am

Apparently the amount of "1" in each line is 2^n starting from second row with n=0, amount of "2" in each line is 2^n starting from third row with n=0, amount of "3" is 2^n starting from fourth row with n=0 and so on... So we always know what numbers in the next one will be.
I still wonder what determines the order...

This post was edited by Dorieus on Apr 24 2013 10:00am

ah good catch, so yeah, just need someone to figure out the order.