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- W2948880189 abstract "The Kolakoski sequence is the unique infinite sequence with values in ${1, 2}$ and first term twems $1, 2, ldots$ which equals the sequence of run-lengths of itself, we call this $K(1, 2).$ We define $K(m, n)$ similarly for $m+n$ odd. A well-known open problem is that its limiting density is one-half. Indeed, not much is known about the Kolakoski sequence. The focus of this paper in on conjectures related to the Kolakoski sequence which are more discrete in nature. We conjecture that a certain doubly infinite family of finite sequences $E_{1, n}left(1^{2^j}, 1^{2j}right)$ has odd length for all $j>0$ and even $n>0.$ We define $cf(m, n, d)$ to be the correlation frequency or limiting probability that terms in $K(m, n)$ which are $d$ apart are equal. We conjecture that the sign of $cf(m, n, d) - 1/2$ is periodic mod $m+n.$ We also discuss extensive empirical evidence for these conjectures." @default.
- W2948880189 created "2019-06-14" @default.
- W2948880189 creator A5073947544 @default.
- W2948880189 date "2017-02-27" @default.
- W2948880189 modified "2023-09-27" @default.
- W2948880189 title "Conjectures related to regularity in the Kolakoski sequence" @default.
- W2948880189 hasPublicationYear "2017" @default.
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