sequence.rb

class Sequence
  def initialize(str)
    @digits = str.chars.map(&:to_i)
  end

  def next
    new_digits = []
    digit_repeats = 1
    @digits.each_cons(2) do |prev, curr|
      if prev == curr
        digit_repeats += 1
      else
        new_digits << digit_repeats << prev
        digit_repeats = 1
      end
    end
    new_digits << digit_repeats << @digits.last
    Sequence.new(new_digits.join)
  end

  def to_s
    @digits.join
  end
end

s = Sequence.new("1")
s.next.to_s #=> "11"
s.next.next.to_s #=> "1211"
s.next.next.next.to_s #=> "111221"