%I #9 Sep 26 2019 08:09:45
%S 1,2,6,6,24,48,120,240,1440,2880,10080
%N a(n) is the minimal product of a positive integer sequence of length n with no duplicate substrings (forward or backward) of length greater than 1, and no self-adjacent terms.
%e a(1) = 1 via [1];
%e a(2) = 2 via [1,2];
%e a(3) = 6 via [1,2,3];
%e a(4) = 6 via [1,2,3,1];
%e a(5) = 24 via [1,2,3,1,4];
%e a(6) = 48 via [1,2,3,1,4,2];
%e a(7) = 120 via [1,2,3,1,4,5,1];
%e a(8) = 240 via [1,2,3,1,4,2,5,1];
%e a(9) = 1440 via [1,2,3,1,4,2,5,1,6];
%e a(10) = 2880 via [1,2,3,1,4,2,5,1,6,2];
%e a(11) = 10080 via [1,2,3,1,4,2,5,1,6,7,1].
%e Examples:
%e [1,1] is invalid because 1 is self-adjacent.
%e [1,2,3,1,2] is invalid because the substring [1,2] appears twice.
%e [1,2,1] is invalid because the substring [1,2] appears twice (once forward and once backward).
%Y Cf. A282164, A282169.
%Y Cf. A282167 is the sum analog.
%K nonn,more
%O 1,2
%A _Peter Kagey_, Feb 07 2017