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A157129
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An analog of the Kolakoski sequence A000002, only now a(n) = (length of n-th run divided by 2) using 1 and 2 and starting with 1,1.
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2
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1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2
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OFFSET
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1,3
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LINKS
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FORMULA
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As for the Kolakoski sequence we suspect Sum_{k=1..n} a(k) = (3/2)*n + o(n).
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EXAMPLE
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The third run is 1,1,1,1, which is of length 4, thus a(3) = 4/2 = 2.
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PROG
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(PARI) w=[1, 1]; for(n=2, 1000, for(i=1, 2*w[n], w=concat(w, 1+(n+1)%2))); w \\ Corrected by Kevin Ryde and Jon Maiga, Jun 11 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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