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

Offset: 1

Author

Clark Kimberling, Aug 19 2008, Aug 25 2008

Keywords

• nonn
• tabl

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.

Examples

			Row 4 (1,1,2,2) determines row 5: (one 1, one 2, two 1's, two 2's).
		

References

• William G. Kolakoski, unpublished note entitled "Kolakoski Series Fan," dated Nov 12, 1993.

Links

• Wikipedia, Kolakoski sequence

Crossrefs

Cf. A000002.