In which Brain teaches Pinky his numbers

Brain begins Pinky's first math lesson by writing "1" on the blackboard, asking "Pinky, do you know what this is?" Pinky responds, "YEP! It's one one!" Brain slaps himself on the forehead. "No Pinky, 'one one' is like this," he writes "11" on the board. "And it's called eleven." Pinky looks confused, "But that's two one..." he says. Brain writes "21" on the board, but before he can speak, Pinky continues, "And that's one two and one one." So Brain writes "1211." Pinky cuts in, "...and that's one one, one two, and two one!" Brain writes "111221"...

If the conversation and blackboard work continues in this fashion, in what number will Brain write the first 4?

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