This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A203810 #23 Nov 19 2017 12:52:01 %S A203810 1,1,1,-1,7,-1,13,-9,199,-53,1937,-373,22871,-2869,4231,-547,134845, %T A203810 -1291,2425919,489967,-10595393,-13913,232472561,9379691,-1023947321, %U A203810 5712079,-2957435363,-89098463,77729577773,93259013,-2326198533397,-139786038869,385098109121 %N A203810 Numerators of s(i) = s(i-1) - (1/i)*sign(s(i-1)) with s(1) = 1. %C A203810 Denominators are given in A203811. %C A203810 Similar to harmonic series, but with signs chosen to minimize the absolute value of the next term. %H A203810 Hugo Pfoertner, <a href="/A203810/b203810.txt">Table of n, a(n) for n = 1..200</a> %H A203810 Hugo Pfoertner, <a href="/A203810/a203810.pdf">Illustration of A203810(i)/A203811(i) for i<=100</a> %H A203810 Hugo Pfoertner, <a href="/A203810/a203810_1.pdf">Illustration of A203810(i)/A203811(i) for even i, i<=500</a> %e A203810 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. %Y A203810 Cf. A203811 (denominators), A203812 (minima of abs(A203810(i)/A203811(i))). %Y A203810 Cf. A001008, A002805 (harmonic numbers). %K A203810 sign,frac %O A203810 1,5 %A A203810 _Hugo Pfoertner_ and _Rainer Rosenthal_, Jan 06 2012