

A203810


Numerators of s(i) = s(i1)  (1/i)*sign(s(i1)) 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
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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)=11/2=1/2. Similar for s(3) and s(4): s(3)=s(2)1/3=1/21/3=1/6, s(4)=1/61/4=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 A040055 A013614
Adjacent sequences: A203807 A203808 A203809 * A203811 A203812 A203813


KEYWORD

sign,frac


AUTHOR

Hugo Pfoertner and Rainer Rosenthal, Jan 06 2012


STATUS

approved



