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 A143589 Kolakoski fan based on A000034 with initial row 1. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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 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 A073203 A073204 Adjacent sequences:  A143586 A143587 A143588 * A143590 A143591 A143592 KEYWORD nonn,tabf AUTHOR Clark Kimberling, Aug 25 2008 STATUS approved

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Last modified November 17 23:16 EST 2018. Contains 317279 sequences. (Running on oeis4.)