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 A118287 #13 Jan 03 2024 06:43:48 %S A118287 1,2,1,3,6,5,6,10,9,10,8,17,16,17,15,12,13,12,28,27,28,26,23,24,23,19, %T A118287 20,19,21,46,45,46,44,41,42,41,37,38,37,39,30,31,30,32,35,34,35,75,74, %U A118287 75,73,70,71,70,66,67,66,68,59,60,59,61,64,63,64,48,49,48,50,53,52,53 %N A118287 A fractal transform of the Lucas numbers: define a(1)=1, then if L(n)<k<=L(n+1) a(k) = L(n+1) - a(k-L(n)) where L(n) = A000032(n). %C A118287 From _Jeffrey Shallit_, Jan 01 2024: (Start) %C A118287 No integer appears three times or more in this sequence. %C A118287 If an integer appears twice, it appears as a(n) and a(n-2) for some n. %C A118287 a(n) = a(n-2) if and only if n belongs to A003231. (observation of Benoit Cloitre) %C A118287 All these and more properties can be proved using the synchronized Fibonacci automaton for a(n), which has 102 states. (End) %H A118287 Benoit Cloitre and Jeffrey Shallit, <a href="https://arxiv.org/abs/2312.11706">Some Fibonacci-Related Sequences</a>, arXiv:2312.11706 [math.CO], 2023-2024. %Y A118287 Cf. A105774, A105669, A000032, A003231. %K A118287 nonn %O A118287 1,2 %A A118287 _Casey Mongoven_, Apr 22 2006