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

1,2

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.

Links

Table of n, a(n) for n=1..100.

Formula

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

Mathematica

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

Prog

(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];

Crossrefs

Cf. A293630, A293811.

Sequence in context: A358005 A078316 A207668 * A055443 A003842 A095771

Adjacent sequences: A293835 A293836 A293837 * A293839 A293840 A293841

Keyword

nonn

Author

Benoit Cloitre, Oct 17 2017

Status

approved