A293838 - OEIS

%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