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

1,1

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

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

Example

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,...

Crossrefs

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

Sequence in context: A051718 A370414 A016472 * A060839 A088204 A100375

Adjacent sequences: A095343 A095344 A095345 * A095347 A095348 A095349

Keyword

nonn

Author

Benoit Cloitre, Jun 03 2004

Status

approved