This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A282168 #23 Jun 18 2025 00:48:43 %S A282168 1,2,4,6,8,10,13,16,19,22,25,29,33,37,41,45,49,53,57,62,67,72,77,82, %T A282168 87,92,97,102,108,114,120,126,132,138,144,150,156,162,168,174,181,188, %U A282168 195,202,209,216,223,230,237,244,251,258,265,273,281,289,297,305,313,321,329,337,345,353 %N A282168 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. %C A282168 This sequence shares first 12 terms with A025224, but then they diverge: a(13) = 33 > 32 = A025224(13). %C A282168 We seem to have a(n) = a(n-1) + a(n-2) - a(n-3) + d(n), where d(n) is 0 or 1. Compare to A282166. - _Max Alekseyev_, Jun 13 2025 %e A282168 [1,2,3,1,2] is invalid because the substring [1,2] appears twice. %e A282168 [1,2,1] is invalid because the substring [1,2] appears twice (once forward and once backward). %e A282168 a(1) = 1 via [1]; %e A282168 a(2) = 2 via [1,1]; %e A282168 a(3) = 4 via [1,1,2]; %e A282168 a(4) = 6 via [1,1,2,2]; %e A282168 a(5) = 8 via [1,1,2,3,1]; %e A282168 a(6) = 10 via [1,1,2,2,3,1]; %e A282168 a(7) = 13 via [1,1,2,2,3,3,1]; %e A282168 a(8) = 16 via [1,1,2,2,3,1,4,2]; %e A282168 a(9) = 19 via [1,1,2,2,3,3,1,4,2]; %e A282168 a(10) = 22 via [1,1,2,2,3,1,4,2,5,1]; %e A282168 a(11) = 25 via [1,1,2,2,3,3,1,4,2,5,1]; %e A282168 a(12) = 29 via [1,1,2,2,3,3,1,4,4,2,5,1]. %Y A282168 Cf. A259280, A282166, A282167, A282193. %K A282168 nonn %O A282168 1,2 %A A282168 _Peter Kagey_, Feb 07 2017 %E A282168 Edited and terms a(13) onward added by _Max Alekseyev_, Feb 05 2025