The string an other is vanishingly rare in english. In contrast another is positively pervasive. I think it would be fair to say that the second has eclipsed the first to the point of making the first.

It is similar to saying every odd week or every even week, only it doesn't matter what number week it is, it only matters that it's every second one. There's a formula: Another = an + other. Think of it as of an article plus the word other that have historically merged into one word. Grammar requires some article before other book; Either the or.

Grammar requires some article before other book; Either the or.