A203810 Numerators of s(i) = s(i-1) - (1/i)*sign(s(i-1)) with s(1) = 1.

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

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: A342603 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