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

Author

Hugo Pfoertner and Rainer Rosenthal, Jan 06 2012

Keywords

• sign
• frac

Comments

Denominators are given in A203811.

Similar to harmonic series, but with signs chosen to minimize the absolute value of the next term.

Examples

			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.
		

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

Crossrefs

Cf. A203811 (denominators), A203812 (minima of abs(A203810(i)/A203811(i))).

Cf. A001008, A002805 (harmonic numbers).