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 A203810 Numerators of s(i) = s(i-1) - (1/i)*sign(s(i-1)) with s(1) = 1. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Denominators are given in A203811. Similar to harmonic series, but with signs chosen to minimize the absolute value of the next term. LINKS 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 EXAMPLE 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. CROSSREFS Cf. A203811 (denominators), A203812 (minima of abs(A203810(i)/A203811(i))). Cf. A001008, A002805 (harmonic numbers). Sequence in context: A013600 A060393 A060394 * A225017 A268919 A040055 Adjacent sequences:  A203807 A203808 A203809 * A203811 A203812 A203813 KEYWORD sign,frac AUTHOR Hugo Pfoertner and Rainer Rosenthal, Jan 06 2012 STATUS approved

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Last modified March 20 23:01 EDT 2018. Contains 300991 sequences. (Running on oeis4.)