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 A346781 #14 Aug 04 2021 10:06:34
%S A346781 1,2,7,64,227,2182,24901,27904,519413,9103082,8410247,207985216,
%T A346781 1106853941,3134651098,85885292267,2808012157952,2944757946677,
%U A346781 402260886146,14238994069127,14850593365952,632726700580207,26229300849325726,25294817897063581,1230908174013784832
%N A346781 a(n) is the numerator of the sum of the first n terms of 1 - 1/3 - 1/5 + 1/7 + 1/9 - 1/11 - 1/13 + ... .
%C A346781 The limit for n->oo of the sum 1 - 1/3 - 1/5 + 1/7 + ... is log(1+sqrt(2))/sqrt(2) (A196525). See there for more information.
%D A346781 Barry Mazur, Chapter IV.1 Algebraic Numbers, page 316, in The Princeton Companion to Mathematics, ed. Timothy Gowers, Princeton University Press, Princeton and Oxford, 2008.
%e A346781 1, 2/3, 7/15, 64/105, 227/315, 2182/3465, 24901/45045, 27904/45045, ...
%o A346781 (PARI) a346781(limit)={my(s=0,b(n)=1/(n*sign(4-(n+2)%8)));forstep(k=1,limit,2,print1(numerator(s+=b(k)),", "))};
%o A346781 a346781(47)
%Y A346781 The corresponding denominators are A025547.
%Y A346781 Cf. A091337, A196525.
%K A346781 nonn,frac
%O A346781 1,2
%A A346781 _Hugo Pfoertner_, Aug 03 2021