Definition:Time-Constructible Function/Definition 2

Definition
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 $1$, $M$ outputs the binary representation of $f \left({n}\right)$ in $O \left({f \left({n}\right)}\right)$ time.

Then $f$ is time-constructible.

Also see

 * Equivalence of Definitions of Turing Machine