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A293630
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"Look to the left" sequence starting with (1, 2): when the sequence has n terms, extend it by appending a(n) copies of a(1..n-1).
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14
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1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2
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OFFSET
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1,2
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COMMENTS
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Stage 1: last term of 1,2 is 2 hence we add 2 copies of the block to the left of the last term (here 1) giving 1,2,1,1.
Stage 2: last term of 1,2,1,1 is 1 hence we add one copy of the block to the left of the last term (here 1,2,1) giving 1,2,1,1,1,2,1.
Stage 3: last term of 1,2,1,1,1,2,1 is 1 hence we add one copy of the block to the left of the last term (here 1,2,1,1,1,2) giving 1,2,1,1,1,2,1,1,2,1,1,1,2.
Iterate the process.
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LINKS
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FORMULA
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It seems that lim_{n->infinity} (a(1) + a(2) + ... + a(n))/n = 1.27526... (see link and A296564).
Because of the previous statement, it seems that the ratio of 2s to 1s in this sequence is 1:2.6329... (see A297927). - Iain Fox, Oct 15 2017
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MATHEMATICA
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f[s_List] := Block[{a = Flatten[s][[-1]], b = Most@ s}, s = Join[s, Flatten@ Table[b, {a}]]]; Nest[f, {1, 2}, 6] (* Robert G. Wilson v, Dec 23 2017 *)
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PROG
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(PARI) v=[1, 2]; for(n=1, 10, l=length(v); w=vector(l-1, i, v[i]); v=concat(v, if(v[l]-1, concat(w, w), w))); a(n)=v[n];
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CROSSREFS
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"Look to the left" sequences: A322423 (seed 1,2,3), A322424 (seed 1,2,3,4), A322425 (seed 1,2,3,4,5).
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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