Looking at a table of minimum stick numbers for knots (table here),
it seems the known upper bound of $2 c(K)$ in terms of the knot crossing number $c(K)$
is realized by the trefoil $3_1$—it requires 6 sticks (see image below) and its crossing number is 3—but not by any other small knot, at least through cursory inspection.
Whence the question in the title: Are there other knots whose minimal stick number reaches the upper
bound of twice its crossing number? This is probably well-known (perhaps well-known to be unknown),
in which case a reference would suffice. Thanks!
Addendum. I found a 12-year old answer to my question in a paper by Eric Furstenberg, Jie Lie, and Jodi Schneider [FLS]:
"Thus far, the trefoil is the only knot to realize Negami’s upper bound of $2c[K]$ on the stick number. Do other such knots exist, and if so, what are their similarities to the trefoil?"
If anyone knows of more recent information, I would appreciate hearing of it. Thanks!
[FLS] "Stick Knots." Eric Furstenberg, Jie Lie, and Jodi Schneider. Chaos, Solitons & Fractals, Vol. 9, No. 4-5, pp. 561-568, 1998. Elsevier link