https://math.stackexchange.com/questions/3279766/sparse-ruler-conjecture On Thursday, July 4, 2019, 08:58:21 PM CDT, ed pegg <ed@mathpuzzle.com> wrote: At Sparse Ruler Conjecture I've posted the Sparse Ruler conjecture. Sparse Ruler Conjecture: If a minimal sparse ruler of length n has m marks, then m-⌈sqrt(3×n+9/4)⌋ ∈ (0,1). I just made an improvement to the list there. One length 188 ruler has gaps as: {0, 1, 2, 3, 5, 12, 21, 30, 47, 64, 81, 98, 115, 132, 148, 149, 156, 164, 172, 180, 185, 186, 187, 188} {1, 1, 1, 2, 7, 9, 9, 17, 17, 17, 17, 17, 17, 16, 1, 7, 8, 8, 8, 5, 1, 1, 1} This expands into a new record setting ruler of length 239. You might be able to see the expansion method {0, 1, 2, 3, 5, 12, 21, 30, 47, 64, 81, 98, 115, 132, 149, 166, 183, 199, 200, 207, 215, 223, 231, 236, 237, 238, 239}{1, 1, 1, 2, 7, 9, 9, 17, 17, 17, 17, 17, 17, 17, 17, 17, 16, 1, 7, 8, 8, 8, 5, 1, 1, 1} That ruler has excess 0 instead of 1. --Ed Pegg Jr | | | | | | | | | | | Sparse Ruler Conjecture Sparse Ruler Conjecture: If a minimal sparse ruler of length $n$ has $m$ marks, then $m - \lceil \sqrt{3 \times... | | | _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun