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%I #13 Jan 03 2024 06:43:48
%S 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 20,19,21,46,45,46,44,41,42,41,37,38,37,39,30,31,30,32,35,34,35,75,74,
%U 75,73,70,71,70,66,67,66,68,59,60,59,61,64,63,64,48,49,48,50,53,52,53
%N 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 From _Jeffrey Shallit_, Jan 01 2024: (Start)
%C No integer appears three times or more in this sequence.
%C If an integer appears twice, it appears as a(n) and a(n-2) for some n.
%C a(n) = a(n-2) if and only if n belongs to A003231. (observation of Benoit Cloitre)
%C All these and more properties can be proved using the synchronized Fibonacci automaton for a(n), which has 102 states. (End)
%H 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 Cf. A105774, A105669, A000032, A003231.
%K nonn
%O 1,2
%A _Casey Mongoven_, Apr 22 2006
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