At http://demonstrations.wolfram.com/SparseRulers/ are sparse rulers to length 1515.  For all of these lengths, with n=length and m=minimal marks,  m - round(sqrt(3*n+9/4))  is either 0 or 1.   The 0/1 pattern to length 1515 is nice, you can see it at  http://demonstrations.wolfram.com/SparseRulers/HTMLImages/index.en/popup_3.j...  . More discussion is at https://math.stackexchange.com/questions/3279766/sparse-ruler-conjecture  and https://math.stackexchange.com/questions/3246000/graceful-graphs-with-valenc...  . In my larger list, bound is true to at least 1790. --Ed Pegg Jr