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A115790
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a(n) = 1 - (floor((n+1)*Pi) - floor(n*Pi)) mod 2.
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3
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0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0
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OFFSET
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0,1
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COMMENTS
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The arithmetic mean 1/(n+1)*sum(a(k)|k=0...n) converges to Pi-3. What is effectively the same: the Cesaro limit (C1) of a(n) is Pi-3.
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LINKS
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FORMULA
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a(n) = 1 - (Floor((n+1)*Pi)-Floor(n*Pi)) mod 2.
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EXAMPLE
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a(6)=0 because 7*Pi=21.99, 6*pi=18.85 and so a(6)=1-(21-18) mod 2 = 0;
a(7)=1 because 8*Pi=25.13 and so a(7)=1-(25-21) mod 2 = 1;
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MATHEMATICA
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Mod[1-(Last[#]-First[#]), 2]&/@(Partition[Floor[Pi #]&/@ Range[ 0, 110], 2, 1]) (* Harvey P. Dale, Oct 12 2012 *)
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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