By the way / On purpose
In conversation, a propósito works like 'by the way' to introduce a related thought. It also means 'on purpose' in other contexts — context makes the meaning clear.
By the way, do you know when the order arrives?
Speaking of what we discussed yesterday, I have news.
—By the way, how is your mother? —Fine, thanks.
By the way, Maria called you.
Speaking of what you're saying, I have an idea.