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

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, 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

Offset

1,4

Comments

This is the first sequence reached in the infinite process described in the 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 121312131312... starting with 1. The letter-to-letter map is 1->1, 2->1, 3->3. See also the comments in A108103. - Michel Dekking, Jan 06 2018

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.

Links

Table of n, a(n) for n=1..105.

Formula

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

Example

A095346 begins: 3,1,3,1,1,1,3,1,3,1,1,1,3,1,1,1,... and length or runs of 3's and 1's are 1,1,1,3,1,1,1,3,1,3,...

Crossrefs

Cf. A064353, A095343, A095344, A095346, A108103.

Sequence in context: A155744 A086869 A348953 * A342671 A132468 A353235

Adjacent sequences: A095342 A095343 A095344 * A095346 A095347 A095348

Keyword

nonn

Author

Benoit Cloitre, Jun 03 2004

Status

approved