Definition:Time-Constructible Function

Definition
A function $f$ is called time-constructible if there exists a positive integer $n_0$ and Turing machine $M$ which, given a string $1^n$ consisting of $n$ ones, stops after exactly $f \left( {n} \right)$ steps for all $n \ge n_0$.

Alternative definition
A function $f$ is called time-constructible if there exists a Turing machine $M$ which, given a string $1^n$, outputs the binary representation of $f \left( {n} \right)$ in $O \left({ f \left( {n} \right) }\right)$ time.