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A078711 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. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
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.
EXAMPLE
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.
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A091654 A127246 A106038 * A338850 A322423 A325494
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Dec 19 2002
STATUS
approved

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Last modified July 21 11:45 EDT 2024. Contains 374472 sequences. (Running on oeis4.)