Perfect Infinitive

Dear members/visitors
I'm kind of torn between two things, Let's say I am writing a letter to a friend to share my thoughts about the holdiays I spent in Scotland, which of them should I use? I guess b is the correct one? Do we pertain here to the relation as in the case of Present Perfect and Present Perfect Continuous tenses? In which situation number a would be correct?

a) I'm sorry for not having been writing to you for such a long time.
b) I'm sorry for not having written to you for such a long time.