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%I #10 Sep 26 2019 08:09:16
%S 1,3,6,7,11,13,17,19,25,27
%N a(n) is the minimal sum 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.
%C Examples:
%C [1,1] is invalid because 1 is self-adjacent.
%C [1,2,3,1,2] is invalid because the substring [1,2] appears twice.
%C [1,2,1] is invalid because the substring [1,2] appears twice (once forward and once backward).
%e a(1) = 1 via [1];
%e a(2) = 3 via [1,2];
%e a(3) = 6 via [1,2,3];
%e a(4) = 7 via [1,2,3,1];
%e a(5) = 11 via [1,2,3,1,4];
%e a(6) = 13 via [1,2,3,1,4,2];
%e a(7) = 17 via [1,2,3,1,4,5,1];
%e a(8) = 19 via [1,2,3,1,4,2,5,1];
%e a(9) = 25 via [1,2,3,1,4,2,5,1,6];
%e a(10) = 27 via [1,2,3,1,4,2,5,1,6,2].
%Y Cf. A259280, A282166, A282168.
%K nonn,more
%O 1,2
%A _Peter Kagey_, Feb 07 2017
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