[seqfan] Re: Noninterfering picket fence seeds

[Ron Hardin]

So far, all even n have equally good shortest solutions that are symmetric, the missing ones below for n=10 and n=12 being
$ check.sh 10 66
 1 7 16 22 32 35 45 51 60 66
$ check.sh 12 89
 1 7 16 22 30 39 51 60 68 74 83 89

which don't turn up below only because they're not lexicographically smallest.

%I A000001
%S A000001 1,2,6,8,18,21,33,38,54,66,83,89,106,124,150,166,190,208
%N A000001 Smallest range 1..a(n) that permits n integers x() in 1..a(n) to exist with (x(i)-x(j)) mod (x(k)-x(j)) nonzero whenever i,j,k are disjoint.
%C A000001 Maximal non-interfering picket-fence seeds: a picket fence extended from any pair in the set encounters no other member of the set
%e A000001 a(1) 1
%e A000001 a(2) 1 2
%e A000001 a(3) 1 3 6
%e A000001 a(4) 1 3 6 8
%e A000001 a(5) 1 4 8 14 18
%e A000001 a(6) 1 4 8 14 18 21
%e A000001 a(7) 1 4 8 14 23 30 33
%e A000001 a(8) 1 5 11 15 24 28 34 38
%e A000001 a(9) 1 10 16 20 23 27 33 42 54
%e A000001 a(10) 1 7 11 17 26 32 40 52 60 66
%e A000001 a(11) 1 7 15 21 30 36 46 58 68 74 83
%e A000001 a(12) 1 7 15 21 30 36 46 58 68 74 83 89
%e A000001 a(13) 1 9 15 24 30 40 52 67 77 83 92 98 106
%e A000001 a(14) 1 10 22 30 36 51 57 68 74 89 95 103 115 124
%e A000001 a(15) 1 7 22 28 36 48 56 69 81 98 107 113 122 138 150
%e A000001 a(16) 1 7 15 27 45 59 65 74 93 102 108 122 140 152 160 166
%e A000001 a(17) 1 13 29 35 44 51 63 81 92 110 122 129 138 144 160 172 190
%e A000001 a(18) 1 19 31 47 53 62 69 81 99 110 128 140 147 156 162 178 190 208
%e A000001 (lexicographically smallest solutions)
%O A000001 1,2

rhhardin at mindspring.com
rhhardin at att.net (either)