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A293838
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"Look once to the left" sequence starting with 1,2 (see comment).
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1
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1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2
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OFFSET
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1,2
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COMMENTS
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Stage 0: we start from 1,2.
Stage 1: we add one copy of the block to the left of the last term (here the block 1) giving 1,2,1.
Stage 2: we add one copy of the block to the left of the last term (here the block 1,2) giving 1,2,1,1,2.
Stage 3: we add one copy of the block to the left of the last term (here the block 1,2,1,1) giving 1,2,1,1,2,1,2,1,1.
Iterate the process.
At stage n there are 2^n+1 terms.
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LINKS
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Table of n, a(n) for n=1..100.
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FORMULA
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(a(1)+a(2)+...+a(n))/n-->1.354... as n-->infty
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MATHEMATICA
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Nest[Join[#, Take[#, Length@ # - 1]] &, {1, 2}, 7] (* Michael De Vlieger, Oct 18 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))); a(n)=v[n];
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CROSSREFS
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Cf. A293630, A293811.
Sequence in context: A342626 A078316 A207668 * A055443 A003842 A095771
Adjacent sequences: A293835 A293836 A293837 * A293839 A293840 A293841
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre, Oct 17 2017
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STATUS
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approved
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