Unknotting number conjecture for connected sums of opposite torus knots

Let $T(2,k)$ be the $(2,k)$-torus link, let $T(2,-k)$ be its mirror image, and let $u(L)$ denote the unknotting number of a link $L$. For an odd integer $k$, consider the connected sum $T(2,k)\ \sharp\ T(2,-k)$. Unknotting number conjecture. For any odd integer $k$,

$$u(T(2,k)\ \sharp\ T(2,-k)) = k-1.$$

This conjectural formula is used to estimate the number of Reidemeister moves needed to transform the diagrams $D_n$ into diagrams with no crossings. The source provides lower bounds for the relevant unknotting numbers but does not establish this formula.