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

1,2

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William G. Kolakoski, unpublished note entitled "Kolakoski Series Fan," dated Nov 12, 1993.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

Example

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

Crossrefs

Cf. A000002.

Sequence in context: A034095 A037811 A091237 * A214774 A320107 A190321

Adjacent sequences: A143474 A143475 A143476 * A143478 A143479 A143480

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 19 2008, Aug 25 2008

Status

approved