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A095345 a(n) is the length of the n-th run in A095346. 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, 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 (list; graph; refs; listen; history; text; internal format)
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: A051997 A155744 A086869 * A132468 A243915 A309307

Adjacent sequences:  A095342 A095343 A095344 * A095346 A095347 A095348

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Jun 03 2004

STATUS

approved

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Last modified October 29 18:30 EDT 2020. Contains 338067 sequences. (Running on oeis4.)