cp's OEIS Frontend

A282167 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.

%I A282167 #17 Jun 16 2025 00:42:24
%S A282167 1,3,6,7,11,13,17,19,25,27,31,35,39,45,47,53,57,63,67,73,77,83,87,95,
%T A282167 99,105,111,117,123,129,135,141,149,153,161,167,175,181,189,195,203,
%U A282167 209,217,223,231,237,247,253,261,269,277,285,293,301,309,317,325,333,341,351,357,367,375,385,393,403,411,421,429,439
%N A282167 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 A282167 For n>=7, we seem to have a(n) = a(n-1) + a(n-2) - a(n-3) + d(n), where d(n) is in {-2, 0, 2}. Compare to A282166. - _Max Alekseyev_, Jun 13 2025
%e A282167 Examples:
%e A282167   [1,1] is invalid because 1 is self-adjacent.
%e A282167   [1,2,3,1,2] is invalid because the substring [1,2] appears twice.
%e A282167   [1,2,1] is invalid because the substring [1,2] appears twice (once forward and once backward).
%e A282167   a(1)  = 1  via [1];
%e A282167   a(2)  = 3  via [1,2];
%e A282167   a(3)  = 6  via [1,2,3];
%e A282167   a(4)  = 7  via [1,2,3,1];
%e A282167   a(5)  = 11 via [1,2,3,1,4];
%e A282167   a(6)  = 13 via [1,2,3,1,4,2];
%e A282167   a(7)  = 17 via [1,2,3,1,4,5,1];
%e A282167   a(8)  = 19 via [1,2,3,1,4,2,5,1];
%e A282167   a(9)  = 25 via [1,2,3,1,4,2,5,1,6];
%e A282167   a(10) = 27 via [1,2,3,1,4,2,5,1,6,2].
%Y A282167 Cf. A259280, A282166, A282168.
%K A282167 nonn
%O A282167 1,2
%A A282167 _Peter Kagey_, Feb 07 2017
%E A282167 Terms a(11) onward from _Max Alekseyev_, Feb 05 2025