I just read the following paper, where an answer can be found:

Youngsik Huh, Seungsang Oh, An upper bound on stick number of knots, J. Knot Theory Ram. 20 (2011), no. 5, 741–747.

There it is shown that the trefoil is the only knot whose stick number equals twice its crossing number. This is a consequence of the authors' main result (Thm. 1.1), which states that any nontrivial knot $K$ satisfies $s(K)\leq \frac{3}{2}(c(K)+1)$ (thus improving Negami's upper bound).

I just read the following paper, where an answer can be found:

Youngsik Huh, Seungsang Oh, An upper bound on stick number of knots, J. Knot Theory Ram. 20 (2011), no. 5, 741–747, doi: 10.1142/S0218216511008966, arXiv: 1512.03592.

There it is shown that the trefoil is the only knot whose stick number equals twice its crossing number. This is a consequence of the authors' main result (Thm. 1.1), which states that any nontrivial knot $K$ satisfies $s(K)\leq \frac{3}{2}(c(K)+1)$ (thus improving Negami's upper bound).