(In reply to
re(2): Low 300s ?? by Justin)
You are quite right. As you say, the 'x+1' can be dispensed with, if we start with a ruler of order x and simply add 1 to each element, to get rid of the leading zero. So we can reduce x=18 to 20 to EN: 217,247,284, presumably with some confidence; we may also surmise that the figures for x=16 and 17 may be amended to EN 178 and 200 respectively, by following the Golomb elements for the corresponding Rulers, plus 1:
1 2 5 12 27 33 57 69 77 116 118 135 151 164 169 178
1 6 8 18 53 57 68 81 82 101 123 139 160 166 169 192 200
Even so, I now agree it has to be accepted that Golomb just gives an upper bound, below which serious searching can begin, rather than a definite answer, as I'd hoped. Given the amount of computation required, no doubt every bit helps!

Posted by broll
on 20100717 15:57:22 