Definition:Time-Constructible Function/Definition 1

Let $f$ be a function.
Let there exist a positive integer $n_0$ and a Turing machine $M$ such that:
Given a string $1^n$ consisting of $n$ instances of $1$, $M$ stops after exactly $f \left({n}\right)$ steps for all $n \ge n_0$.
Then $f$ is time-constructible.