SequenceProblem.scala

def makeNextSequence(
  previousSeq: List[Int],
  currentSubSeq: List[Int] = List.empty,
  accumulatedSeq: List[List[Int]] = List.empty
): List[Int] = {
  previousSeq match {
    case head :: tail if currentSubSeq.isEmpty =>
      makeNextSequence(tail, List(head), accumulatedSeq)
    case head :: tail if head != currentSubSeq.head =>
      makeNextSequence(tail, List(head), accumulatedSeq :+ currentSubSeq)
    case head :: tail if head == currentSubSeq.head =>
      makeNextSequence(tail, currentSubSeq :+ head, accumulatedSeq)
    case Nil =>
      val finalAccumulated = accumulatedSeq :+ currentSubSeq
      val nextSeq = finalAccumulated flatMap { subSeq =>
        List(subSeq.size, subSeq.head)
      }
      println(nextSeq.mkString(" "))
      nextSeq
  }
}

Here's this function in action on the Scala console:

scala> (1 to 10).foldLeft(List(1)) { case (result, _) => makeNextSequence(result) }
1 1
2 1
1 2 1 1
1 1 1 2 2 1
3 1 2 2 1 1
1 3 1 1 2 2 2 1
1 1 1 3 2 1 3 2 1 1
3 1 1 3 1 2 1 1 1 3 1 2 2 1
1 3 2 1 1 3 1 1 1 2 3 1 1 3 1 1 2 2 1 1
1 1 1 3 1 2 2 1 1 3 3 1 1 2 1 3 2 1 1 3 2 1 2 2 2 1