Ugly number implementation in Scala
First off, I'd like to mention, that my Scala experience is limited, so please do point out any errors.

You should implement your algorithm in it's own class implementing an appropriate interface/trait (probably Iterator, but there may be better ones).

That would also avoid having the awkward hard-coded limit to 11 elements in the main algorithm.

I'm not a fan of the repeated code for the three base numbers. Off the top of my head I'm not sure how to avoid it, but would assume it would include using case classes.

You should also have a look at your variable names. You have a mixture of short cryptic names (n, i3, etc.) and two different styles (camel case and underlines). You should always use descriptive names (maxIterations, index3) and use a single style (preferably camel case as this is the convention for Scala).

BTW, List has a min method, so there is no need to roll your own:

val nextUglyNumber = List(next_multiple_2, next_multiple_3, next_multiple_5).min;