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 A223709 #21 Oct 01 2022 00:11:53 %S A223709 9,4,2,8,6,9,2,3,6,7,8,4,1,1,1,4,6,0,1,9,0,0,8,7,6,5,4,1,5,9,4,8,2,8, %T A223709 0,1,5,0,2,9,9,0,8,8,4,6,9,6,3,5,5,3,1,5,8,2,5,1,5,5,4,1,4,6,2,6,3,8, %U A223709 6,7,0,2,1,6,4,9,8,1,9,5,7,5,0,9,9,5,3 %N A223709 Decimal expansion of (Pi-1)*(2*Pi-1)/12. %C A223709 Let p = sum(sin(k)/k, k>=1) = (Pi-1)/2 (A096444) and q = sum(sin(k/2)/k, k>=1) = (2*Pi-1)/4, then A223709 = (2/3)*p*q. %C A223709 This is the case h=1 in sum(sin(k/h)/k^3, k>=1) = (h*Pi-1)*(2h*Pi-1)/(12*h^3) = ((h*Pi-1)/(2h))*((2h*Pi-1)/(4h))*(2/(3h)), where (j*Pi-1)/(2j) = sum(sin(k/j)/k, k>=1) and 1/j is real but not an integer multiple of 2Pi. %D A223709 Tom M. Apostol, Calculus, Vol. 1, John Wiley & Sons, 1967 (2nd ed.). This constant is the case s=1, t=3 in sum(sin(n*s)/n^t, n>=1), see p. 409. %H A223709 Vincenzo Librandi, <a href="/A223709/b223709.txt">Table of n, a(n) for n = 0..1000</a> %H A223709 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a> %F A223709 Equals sum(sin(k)/k^3, k>=1). %e A223709 0.9428692367841114601900876541594828015029908846963553... %t A223709 RealDigits[(Pi - 1) (2 Pi - 1)/12, 10, 90][[1]] %Y A223709 Cf. A096418, A096444, A217909, A223710. %K A223709 nonn,cons %O A223709 0,1 %A A223709 _Bruno Berselli_, Mar 26 2013