For a 13 year old I would recommend no programming languages at all , Instead it's better to start with mathematics and problem solving as that is the core to be a good developer or programmer.
I beg to disagree. While this may hold true for someone pursuing a serious CS course or a career, the OP's likely intention is a gentle introduction to programming for a child.
Moreover, in my experience with having exposed 7~10 year old kids to Scratch and a bit of Python, I have seen them demonstrate a noticeable interest in mathematics (after, as compared to before). With something such as Scratch, which is more a learning aid, than a serious conventional programming language, it is so easy for them to build stuff almost immediately - like, their own adding machine, or even simple calculators. I feel this naturally piques their interest in mathematics and logic.
If they are truly hooked, this still leaves the kid with a choice to pursue CS or programming further and move on to greater things and along the way learn more advanced math and formal logic.
To sum up, I think math and programming complement each other quite nicely. One doesn't necessarily need to learn one before the other, unless you pursue a formal CS course.
Of course, basic arithmetic always helps. But you would expect a 13-year old to have some command over it already.