I've verified the Sparse Ruler conjecture to at least 1017.  Sparse Ruler Conjecture: If a minimal sparse ruler of length n has m marks, then m − round(sqrt(3×n+9/4))∈(0,1). Anyone that would like my list of best known sparse rulers to length 1200, please contact me.  The only possible counterexample under 1200 is at 1018 at the moment.    https://math.stackexchange.com/questions/3279766/sparse-ruler-conjecture   --Ed Pegg Jr