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A365819
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a(n) = a(n-1) - 1 + floor(median(a) - mean(a)) where a(0) = 0, a(1) = 1, and median(a) and mean(a) are respectively the median and mean of all previous terms.
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3
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0, 1, 0, -2, -3, -4, -5, -7, -8, -9, -10, -11, -12, -13, -15, -17, -19, -21, -22, -23, -24, -25, -26, -27, -27, -27, -27, -27, -28, -29, -31, -33, -36, -39, -43, -47, -51, -54, -57, -59, -61, -63, -64, -65, -65, -65, -65, -64, -63, -61, -58, -55, -51, -47, -43, -39, -35, -31, -28, -25, -22, -19
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OFFSET
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0,4
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COMMENTS
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The median of an even number of terms is taken as the mean of its middle two values, (x+y)/2.
The sequence seems to present a chaotic pattern. What is its asymptotic behavior?
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LINKS
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Thomas Scheuerle, Plot n = 0..200000, blue: a(n)/10, red: mean(a(0)..a(n)), orange: 10*(median(a(0)..a(n))-mean(a(0)..a(n))). We observe new emergent chaos after periods of apparent calming.
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MATHEMATICA
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a = {0, 1};
Do[AppendTo[a, Last[a] - 1 + Floor[Median[a] - Mean[a]]], {j, 1, 100}]
a[[1 ;; 100]]
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PROG
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(MATLAB)
a = [0 1];
for n = 3:max_n
a(n) = a(n-1) - 1 + floor(median(a) - mean(a));
end
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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