In the context of Turing machines, the output is really a _binary_ string, not a string of arbitrary characters. So in a sense, those two programs are the same

In the context of Turing machines, the output is really a _binary_ string, not a string of arbitrary characters. So in a sense, those two programs are the same thing. But of course, the Kolmogorov complexity of any number n is bounded by log(n) + c.