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A078711
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Sequence is S(infinity), where S(1)={1,2,3}, S(n+1)=S(n)S'(n) and S'(n) is obtained from S(n) by changing last term using the cyclic permutation 1->2->3->1.
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3
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1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 2, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 2, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 2, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 2, 1, 2, 3, 1, 2, 1, 1, 2, 3, 1, 2, 2, 1, 2, 3, 1, 2, 1, 1, 2, 3
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OFFSET
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1,2
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LINKS
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FORMULA
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Lim_{n->infinity} Sum_{i=1..n} a(i)/n = 37/21; density of 1's is 3/7; density of 2's is 8/21; density of 3's is 4/21.
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EXAMPLE
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Concatenating 1,2,3 gives 1,2,3,1,2,3; changing the last term 3 to 1 gives the first 6 terms: 1,2,3,1,2,1. Concatenating those 6 terms: 1,2,3,1,2,1,1,2,3,1,2,1; replacing the last term 1 with 3 gives the first 12 terms: 1,2,3,1,2,1,1,2,3,1,2,2.
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MATHEMATICA
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A078711list[i_]:=Nest[Join[#, Most[#], {Mod[Last[#], 3]+1}]&, Range[3], i];
A078711list[6] (* Each iteration doubles the number of terms *) (* Paolo Xausa, Aug 31 2023 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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