|
%I #6 Jan 16 2013 18:52:11
%S 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,
%T 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,
%U 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
%N Kolakoski Fan.
%C (1) Does every row occur infinitely many times as a segment of A000002?
%C (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.
%C Arises from the Kolakoski sequence, K(n)=A000002(n), as follows:
%C row 1: 1
%C row 2: 2
%C row 3: 2 2
%C row 4: 1 1 2 2
%C row 5: 1 2 1 1 2 2,
%C 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.
%D William G. Kolakoski, unpublished note entitled "Kolakoski Series Fan," dated Nov 12, 1993.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Kolakoski_sequence">Kolakoski sequence</a>
%e Row 4 (1,1,2,2) determines row 5: (one 1, one 2, two 1's, two 2's).
%Y Cf. A000002.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Aug 19 2008, Aug 25 2008
|
