A143589 Kolakoski fan based on A000034 with initial row 1.

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

Offset

1,2

Comments

Conjecture (following Benoit Cloitre's conjecture at A111090): if L(n) is the number (assumed finite) of terms in row n of K, then L(n)*(2/3)^n approaches a constant. (L= A143590.)

Links

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

Formula

Introduced here is an array K called the "Kolakoski fan based on a sequence s with initial row w": suppose that s=(s(1),s(2),...) is a sequence of 1's and 2's and that w=(w(1),w(2),...) is a finite or infinite sequence of 1's and 2's. Assume that s(1)=w(1) and that if w(1)=1 then s contains at least one 2. Row 1 of the array K is w. Subsequent rows are defined inductively: the first term of row n is s(n) and the remaining terms are defined by Kolakoski substitution; viz., each number in row n-1 tells the string-length (1 or 2) of the next string in row n, each term being either 1 or 2.

Example

s=(1,2,1,2,1,2,1,2,...) and w=1, so the first 7 rows are
1
2
1 1
2 1
1 1 2
2 1 2 2
1 1 2 1 1 2 2

Crossrefs

Cf. A000002, A143477, A143490.

Sequence in context: A097305 A120675 A072699 * A003651 A325028 A073203

Adjacent sequences: A143586 A143587 A143588 * A143590 A143591 A143592

Keyword

nonn,tabf

Author

Clark Kimberling, Aug 25 2008

Status

approved