The indefinite article a becomes an when it precedes a word beginning with a vowel sound. Similar conventions can be found in thy → thine and the now-archaic my → mine.
Aside from these three examples, are there any other words that take on a special form when they proceed a vowel sound?
I'm aware that some people consider amongst to be a prevocalic form of among, but this usage does not seem to be universal, and furthermore doesn't follow with similar word pairs such as amid/amidst or while/whilst.