A very simple approach to find the first number of the first gap would be the following:
int[] existingNumbers = /* extract all numbers from all filenames and order them */
var allNumbers = Enumerable.Range(0, 1000000);
var result = allNumbers.Where(x => !existingNumbers.Contains(x)).First();
This will return 1,000,000 if all numbers have been used and no gaps exist.
This approach has the drawback that it performs rather badly, as it iterates existingNumbers
multiple times.
A somewhat better approach would be to use Zip:
allNumbers.Zip(existingNumbers, (a, e) => new { Number = a, ExistingNumber = e })
.Where(x => x.Number != x.ExistingNumber)
.Select(x => x.Number)
.First();
An improved version of DuckMaestro's answer that actually returns the first value of the first gap - and not the first value after the first gap - would look like this:
var tmp = existingNumbers.Select((x, i) => new { Index = i, Value = x })
.Where(x => x.Index != x.Value)
.Select(x => (int?)x.Index)
.FirstOrDefault();
int index;
if(tmp == null)
index = existingNumbers.Length - 1;
else
index = tmp.Value - 1;
var nextNumber = existingNumbers[index] + 1;