Using a tabu search procedure, I have found a solution for $|P|=17$, namely ${1, 11, 18, 25, 31, 32, 33, 36, 44, 51, 58, 65, 69, 70, 77, 84, 91}$. I don't know if this is optimal.

Using a tabu search procedure, I have found a solution for $|P|=17$, namely ${1, 11, 18, 25, 31, 32, 33, 36, 44, 51, 58, 65, 69, 70, 77, 84, 91}$. I don't know if this is optimal.

EDIT: Found a solution for $|P|=16$, namely $$10, 15, 22, 29, 36, 43, 53, 55, 56, 57, 58, 68, 73, 74, 84, 91$$

Using a tabu search procedure, I have found a solution for $|P|=17$, namely ${1, 11, 18, 25, 31, 32, 33, 36, 44, 51, 58, 65, 69, 70, 77, 84, 91}$. I don't know if this is optimum.

Using a tabu search procedure, I have found a solution for $|P|=17$, namely ${1, 11, 18, 25, 31, 32, 33, 36, 44, 51, 58, 65, 69, 70, 77, 84, 91}$. I don't know if this is optimal.