A095346 a(n) is the length of the n-th run of A095345.

3, 1, 3, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 1

Offset: 1

Author

Benoit Cloitre, Jun 03 2004

Keywords

• nonn

Comments

This is the second sequence reached in the infinite process described in A066983 comment line.

(a(n)) is a morphic sequence, i.e., a letter to letter projection of a fixed point of a morphism. The morphism is 1->121,2->3,1,3->313. The fixed point is the fixed point 3131213131213... starting with 3. The letter-to-letter map is 1->1, 2->1, 3->3. See also COMMENTS of A108103. - Michel Dekking, Jan 06 2018

Examples

			A095345 begins : 1,1,1,3,1,1,1,3,1,3,...,.. and length or runs of 1's and 3's are 3,1,3,1,1,1,...
		

References

• F. M. Dekking: "What is the long range order in the Kolakoski sequence?" in: The Mathematics of Long-Range Aperiodic Order, ed. R. V. Moody, Kluwer, Dordrecht (1997), pp. 115-125.

Crossrefs

Cf. A064353, A095343, A095344, A095345, A108103.

Formula

a(n)=3 if n=1+2*floor(phi*k) for some k where phi=(1+sqrt(5))/2, else a(n)=1. [Benoit Cloitre, Mar 02 2009]