Crossing-number conjecture for Chebyshev degrees of common difference two

Let $T_n$ denote the degree-$n$ Chebyshev polynomial of the first kind. For an odd integer $i\ge 3$, the difference-two crossing-number conjecture. The parametrization

$$(T_i,T_{i+2},T_{i+4})$$

parametrizes a knot with crossing number $i+1$. This assertion appears in the paper's open-problems section as a pattern suggested by the tabulated Chebyshev-knot examples; no proof or resolution is supplied.