I actually took information theory but this is more of an issue algorithmic information theory - something I have not studied all that much. Though still, I think you are probably right since Kolgomorov complexity refers to descriptive complexity of an object. And here you can give a much shorter description of all of consecutive natural numbers.

This is very interesting to me because intuitively one would think that both are problems involving infinity and hence I lazily thought that they would both have the same complexity.