ROTE / rōt / noun: mechanical or habitual repetition of something to be learned. "a poem learned by rote in childhood"
synonyms: mechanically, automatically, unthinkingly, mindlessly; See Google rote
Most often used in the expression "learned by rote" to mean learning something through repetition. I have never heard it applied to writing out something over and over again. It usually refers to memorizing the content of that which is repeated, for example learning lines of dialogue for a play or learning a prayer by repeating it over and over again. It's the closest I can think of, and does apply to learning something by repetition.
