The problem is entirely one of forming a hypothesis and testing it.
So, we have
176517661768. Ok. The first hypothesis is that the first number is one digit long. That would be a
1. This would mean that I expect the next number to be either a
3 (if the hole is a
2). Lets check that out.
1 - got it.
7 - not a 2 or a 3.
Ok, lets throw that out.
The second hypothesis is that the first number is two digits long. That would be a
17. This would mean that I expect the number to be
17 - got it
65 - not 18 or 19.
Lets try this again. It might be three digits long. That would mean
176 - got it
517 - not a 177 or 178.
Lets try this yet again. It might be four digits long.
1765 - got it
1766 - still matching with the hypothesis
1768 - still matching with the hypothesis (and we have a hole, set that aside)..
Figuring out how to do the appropriate substrings or stream processing is left as an exercise to the reader for their chosen language. This will likely fall into the approach where you are writing a type of state machine where you are only going forward and testing for two possible conditions - the next value or the next value plus one (and once you find a situation where you've accepted next value plus one, all future states have only one acceptance test - that of next value).