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 A091007 #37 Feb 16 2025 08:32:52
%S A091007 1,4,2,4,7,4,1,7,7,8,4,2,9,9,8,0,8,8,9,7,6,1,5,4,7,8,0,6,8,8,9,2,3,4,
%T A091007 1,5,2,8,0,2,0,6,6,3,3,4,6,0,1,8,1,8,0,4,0,6,5,7,2,4,5,7,7,3,1,3,7,1,
%U A091007 1,3,8,6,3,0,2,1,0,3,1,9,6,5,8,1,5,4,9,9,2,0,8,4,9,8,5,1,7,6,6,3,1,1
%N A091007 Decimal expansion of Sum_{n>=1} arccot(n^2).
%H A091007 G. C. Greubel, <a href="/A091007/b091007.txt">Table of n, a(n) for n = 1..10000</a>
%H A091007 George Boros and Victor H. Moll, <a href="http://scientia.mat.utfsm.cl/archivos/vol11/Art2.pdf">Sums of arctangents and some formulas of Ramanujan</a>, Scientia, Ser. A: Math. Sci., Vol. 11 (2005) pp. 13-24, MR2196063, eq. (1.3).
%H A091007 A. Sarkar, <a href="https://www.jstor.org/stable/2324940">The sum of arctangents of reciprocal squares</a>, Amer. Math. Monthly, 98, (1990), 652-653.
%H A091007 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/InverseCotangent.html">Inverse Cotangent</a>.
%F A091007 Decimal expansion of transcendental number arccot((1 + t)/(1 - t)) where t=cot(Pi*sqrt(2)/2) tanh(Pi*sqrt(2)/2). - _Artur Jasinski_, Sep 25 2008
%F A091007 Equals Sum_{k>=1} (-1)^(k+1)*zeta(4*k-2)/(2*k-1). - _Amiram Eldar_, Mar 25 2021
%e A091007 1.424741778429980889761547806889234152802066334601818040657245773...
%t A091007 t = Cot[Pi Sqrt[2]/2] Tanh[Pi Sqrt[2]/2]; s = ArcCot[(1 + t)/(1 - t)]; RealDigits[N[s, 102]] (* _Artur Jasinski_, Sep 25 2008 *)
%o A091007 (PARI) default(realprecision, 100); {t = cotan(Pi/sqrt(2))*tanh(Pi/sqrt(2))}; atan((1-t)/(1+t)) \\ _G. C. Greubel_, Feb 01 2019
%o A091007 (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Arctan((1-Cot(Pi(R)/Sqrt(2))*Tanh(Pi(R)/Sqrt(2)))/(1+Cot(Pi(R)/Sqrt(2))*Tanh(Pi(R)/Sqrt(2)))); // _G. C. Greubel_, Feb 01 2019
%o A091007 (Sage) t = cot(pi/sqrt(2))*tanh(pi/sqrt(2)); numerical_approx(atan((1-t)/(1+t)), digits=100) # _G. C. Greubel_, Feb 01 2019
%K A091007 nonn,cons
%O A091007 1,2
%A A091007 _Eric W. Weisstein_, Dec 13 2003