A157196 a(n) = (1/2)*(sum of elements of n-th run) using 1 and 2 starting with 1,1.

1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1

Offset: 1

Author

Benoit Cloitre, Feb 24 2009

Keywords

• nonn

Comments

We conjecture that the density of 1's in the sequence approaches 2/3 as n -> infinity. This conjecture is proved in the paper of Shallit.

Examples

			Write the sums of elements in each run, you obtain: 2,2,4,2,2,2,2,4,2,2,4,2,2,4,4,... dividing by 2 you get: 1,1,2,1,1,1,1,2,1,1,2,1,1,2,2,... the sequence itself.
		

Links

• Daniel Hoyt, Visual representation of the sequence in the style of the Kolakoski sequence.
• Daniel Hoyt, Representing the sequence visually.
• Jeffrey Shallit, Cloitre's Self-Generating Sequence, arXiv:2501.00784 [math.CO], 2025.

Crossrefs

Cf. A000002, A157129, A336810.

Programs

Maple

mx:= 1000: l:= [1$2]: a:= n-> l[n]:
for h from 2 while nops(l)Alois P. Heinz, May 31 2012

Extensions

More terms from Alvin Hoover Belt, May 31 2012