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 A355921 #20 Aug 06 2024 05:41:40
%S A355921 1,4,0,5,8,6,9,2,9,8,2,8,7,7,8,0,9,1,1,2,5,5,3,9,8,6,1,7,5,6,6,5,1,4,
%T A355921 7,2,3,1,2,1,4,4,2,1,9,0,9,1,9,1,4,4,3,5,8,8,0,8,1,3,4,9,2,0,5,1,9,4,
%U A355921 8,9,2,8,6,0,9,2,1,5,5,3,4,1,0,7,8,5,6
%N A355921 Decimal expansion of Sum_{k>=1} (1/k)*arctan(1/k).
%H A355921 Mathematics Stack Exchange, <a href="https://math.stackexchange.com/questions/2581766/converting-the-sum-sum-limits-n-1-infty-frac1n-cot-1n-to-an-integ">Converting the sum: Sum_{n=1..oo}(1/n) * cot^(-1)(n) to an integral</a>, 2017.
%H A355921 Mathematics Stack Exchange, <a href="https://math.stackexchange.com/questions/4187454/summing-an-arctangent-series">Summing an Arctangent Series</a>, 2021.
%H A355921 Michael Ian Shamos, <a href="https://citeseerx.ist.psu.edu/pdf/ae33a269baba5e8b1038e719fb3209e8a00abec5">Shamos's Catalog of the Real Numbers</a>, 2011, p. 428.
%H A355921 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SineIntegral.html">Sine Integral</a>.
%F A355921 Equals Sum_{k>=1} arccot(k)/k.
%F A355921 Equals Sum_{k>=1} (-1)^(k+1)*zeta(2*k)/(2*k-1).
%F A355921 Equals (1/2) * Integral_{x=0..1} (coth(Pi*x)*Pi/x - 1/x^2) dx.
%F A355921 Equals Integral_{x>=0} Si(x)/(exp(x)-1) dx, where Si(x) is the sine integral function.
%F A355921 Equals -Integral_{x>=0} sin(x)*log(1-exp(-x))/x dx.
%e A355921 1.40586929828778091125539861...
%t A355921 RealDigits[N[Sum[ArcTan[1/k]/k, {k, 1, Infinity}], 30], 10, 27][[1]]
%o A355921 (PARI) default(realprecision, 200); sumalt(k=1,(-1)^(k+1)*zeta(2*k)/(2*k-1)) \\ _Vaclav Kotesovec_, Jul 21 2022
%Y A355921 Cf. A091007, A265011, A343469, A343470, A352619, A355922.
%K A355921 nonn,cons
%O A355921 1,2
%A A355921 _Amiram Eldar_, Jul 21 2022
%E A355921 More terms from _Jinyuan Wang_, Jul 21 2022