I've looked through it with Regexp::Debugger.

Maybe (probably) I'm misunderstanding the question, but in your sample data, the hundred groups in each line seem to be the same. i.e. $1 + 1 will always not equal $2 in this data, for each line.

I think the second point is about the spaces. When the regex matches, it skips a space, so misses out on matching the next number to the first part of the regex.

For example, this inserts a newline before the 200s start:

#!/usr/bin/perl
use strict;
use warnings;
#use Regexp::Debugger;

while( <DATA> ) {
    s[\s(\d+)\d\d\K\s(?=(\d+)\d\d)]{
        $1 + 1 == $2 ? "\n" : ' '
    }ge;
    print;
}

__DATA__
105 106 107 108 109 110 211 212 213
1115 1116 1117 1118 1119 1120 1121 1122 1123
12345 12346 12347 12348 12349 12350 12351 12353
[download]

But when you change the data to:

105 106 107 108 109 210 211 212 213
1115 1116 1117 1118 1119 1120 1121 1122 1123
12345 12346 12347 12348 12349 12350 12351 12353
[download]

the first part of the regex doesn't match the 109, because the match fails on the first space.

Apologies if I'm way off!