A293838 "Look once to the left" sequence starting with 1,2 (see comment).

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

Offset: 1

Author

Benoit Cloitre, Oct 17 2017

Keywords

• nonn

Comments

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.

Crossrefs

Cf. A293630, A293811.

Programs

Mathematica

Nest[Join[#, Take[#, Length@ # - 1]] &, {1, 2}, 7] (* Michael De Vlieger, Oct 18 2017 *)

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];

Formula

Limit_{n->oo} (a(1) + a(2) + ... + a(n))/n = 1.354....