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A078978
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Sequence is S(oo), where S(1)={1,2,3,4}, S(n+1)=S(n)S'(n) and S'(n) is obtained from S(n) by changing its last term using the cyclic permutation 1->2->3->4->1.
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2
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1, 2, 3, 4, 1, 2, 3, 1, 1, 2, 3, 4, 1, 2, 3, 2, 1, 2, 3, 4, 1, 2, 3, 1, 1, 2, 3, 4, 1, 2, 3, 3, 1, 2, 3, 4, 1, 2, 3, 1, 1, 2, 3, 4, 1, 2, 3, 2, 1, 2, 3, 4, 1, 2, 3, 1, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 1, 1, 2, 3, 4, 1, 2, 3, 2, 1, 2, 3, 4, 1, 2, 3, 1, 1, 2, 3, 4, 1, 2, 3, 3, 1, 2, 3, 4, 1, 2, 3, 1, 1
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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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Limit_{n->oo} (Sum_{i=1..n} a(i))/n = 133/60; density of 1's is 19/60; density of 2's is 17/60; density of 3's is 4/15; density of 4's is 2/15.
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EXAMPLE
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Concatenate 1,2,3,4 gives 1,2,3,4,1,2,3,4 change 4 -> 1, hence first 8 terms are 1,2,3,4,1,2,3,1. Concatenate again: 1,2,3,4,1,2,3,1,1,2,3,4,1,2,3,1 change 1->2, hence first 16 terms are 1,2,3,4,1,2,3,1,1,2,3,4,1,2,3,2.
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MATHEMATICA
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A078978list[i_]:=Nest[Join[#, Most[#], {Mod[Last[#], 4]+1}]&, Range[4], i];
A078978list[5] (* 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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