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A203810
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Numerators of s(i) = s(i-1) - (1/i)*sign(s(i-1)) with s(1) = 1.
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3
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1, 1, 1, -1, 7, -1, 13, -9, 199, -53, 1937, -373, 22871, -2869, 4231, -547, 134845, -1291, 2425919, 489967, -10595393, -13913, 232472561, 9379691, -1023947321, 5712079, -2957435363, -89098463, 77729577773, 93259013, -2326198533397, -139786038869, 385098109121
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OFFSET
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1,5
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COMMENTS
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Denominators are given in A203811.
Similar to harmonic series, but with signs chosen to minimize the absolute value of the next term.
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LINKS
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Hugo Pfoertner, Table of n, a(n) for n = 1..200
Hugo Pfoertner, Illustration of A203810(i)/A203811(i) for i<=100
Hugo Pfoertner, Illustration of A203810(i)/A203811(i) for even i, i<=500
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EXAMPLE
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s(1)=1, to minimize abs(s(2)) 1/2 has to be subtracted. s(2)=1-1/2=1/2. Similar for s(3) and s(4): s(3)=s(2)-1/3=1/2-1/3=1/6, s(4)=1/6-1/4=-1/12. Since s(4) is negative s(5)=s(4)+1/5=-1/12+1/5=7/60. The numerators of s(1)...s(5) are 1, 1, 1, -1, 7 and the corresponding denominators are 1, 2, 6, 12, 60.
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CROSSREFS
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Cf. A203811 (denominators), A203812 (minima of abs(A203810(i)/A203811(i))).
Cf. A001008, A002805 (harmonic numbers).
Sequence in context: A013600 A060393 A060394 * A225017 A040055 A013614
Adjacent sequences: A203807 A203808 A203809 * A203811 A203812 A203813
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KEYWORD
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sign,frac
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AUTHOR
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Hugo Pfoertner and Rainer Rosenthal, Jan 06 2012
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STATUS
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approved
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