I double majored in math and computer science but otherwise, there would have been no requirement for me to take any programming classes. As my programming skills and mathematical problem-solving skills developed, they both informed one another. I often turned to my programming experience for making combinatorial arguments and the mathematician in me made sure I'd thought through all possible ways a program could progress.
As far as consistent problems, I'd have to second Michael Hoffman's answer. In my experience, mathematicians have little trouble solving a programming problem but actually getting it into code can be an obstacle. Knowing what the answer is doesn't help you if you can't write it down within the confines of whatever language you're using. Planning ahead and pseudocode are both really helpful for getting around this. Plus, this is probably familiar to mathematicians who don't code - I find myself writing down some mathematics for the first termtime, then realising that somehow I'm not saying what I really want to say or that I'm not even saying it correctly.
