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%I #11 Oct 22 2022 16:18:37
%S 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,
%T 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,
%U 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
%N "Look once to the left" sequence starting with 1,2 (see comment).
%C Stage 0: we start from 1,2.
%C Stage 1: we add one copy of the block to the left of the last term (here the block 1) giving 1,2,1.
%C 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.
%C 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.
%C Iterate the process.
%C At stage n there are 2^n+1 terms.
%F Limit_{n->oo} (a(1) + a(2) + ... + a(n))/n = 1.354....
%t Nest[Join[#, Take[#, Length@ # - 1]] &, {1, 2}, 7] (* _Michael De Vlieger_, Oct 18 2017 *)
%o (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];
%Y Cf. A293630, A293811.
%K nonn
%O 1,2
%A _Benoit Cloitre_, Oct 17 2017
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