Structure of Ramsey gaps and geometric building blocks

Determine whether the Ramsey-gap sequence g(t)=R(3,t)−R(3,t−1) has a discernible pattern and whether it is connected to a sequence of basic admissible gadgets in the triangle-free geometric blocking problem.

Background

The authors define the Ramsey-gap sequence g(t)=R(3,t)−R(3,t−1) and note that its average order is Θ(t/log t), using the known estimate R(3,t)=Θ(t²/log t). They ask whether the sequence has additional structure and whether its increments can serve as or arise from geometric building blocks for constructing triangle-free-crossing segment families that block points.