A143477 - OEIS

A143477

Kolakoski Fan.

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

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OFFSET

1,2

COMMENTS

(1) Does every row occur infinitely many times as a segment of A000002?

(2) In Kolakoski's note, the initial 1 appears at the bottom, centered, with 2 just above and successive rows arise as branches so that the array resembles a handheld fan.

Arises from the Kolakoski sequence, K(n)=A000002(n), as follows:

row 1: 1

row 2: 2

row 3: 2 2

row 4: 1 1 2 2

row 5: 1 2 1 1 2 2,

and so on, where the first term in row n is K(n) and row n-1 tells how many of each kind (1 or 2) to write in row n.

REFERENCES

William G. Kolakoski, unpublished note entitled "Kolakoski Series Fan," dated Nov 12, 1993.

LINKS

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

Wikipedia, Kolakoski sequence