Puzzle ZGWK 

Workings

Hint
Remove the spaces from the sequence first.

Answer
1301311.

Reasoning
Removing spaces from the original sequence gives:

   1 23 124 1251 26127 128129

   123124125126127128129

Now adding spaces back in, in the correct place:

   123 124 125 126 127 128 129

So the next few terms should be 130 131 132, so add these to the end:

   123 124 125 126 127 128 129 130 131 132

Now remove the spaces again:

   123124125126127128129130131132

No break the sequence into chunks of increasing size - as per the original question:

   1 23 124 1251 26127 128129 1301311

So the missing term is 1301311.