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 A386732 #13 Aug 03 2025 03:28:03
%S A386732 0,0,0,0,4,4,3,9,4,3,8,8,3,8,9,7,3,2,9,3,1,6,1,9,7,9,3,7,0,8,8,6,1,0,
%T A386732 4,5,9,0,2,9,4,1,1,8,5,0,4,7,6,8,8,5,1,8,1,8,5,7,0,2,5,0,0,7,5,2,9,5,
%U A386732 8,9,0,0,4,2,4,9,5,9,9,5,3,8,0,8,1,2,9,4,5,1,1,5,5,0,3,9,2,3,2,5,1,8,3,8
%N A386732 Decimal expansion of Integral_{x>=2} 1/(x^12-1) dx.
%H A386732 Jason Bard, <a href="/A386732/b386732.txt">Table of n, a(n) for n = 0..1003</a>
%H A386732 Michael I. Shamos, <a href="http://euro.ecom.cmu.edu/people/faculty/mshamos/cat.pdf">A catalog of the real numbers</a>, (2007). See p. 21.
%F A386732 Equals (1/22528) * hypergeometric(11/12, 1; 23/12; 1/4096).
%F A386732 Equals (-6*Pi - 4*sqrt(3)*Pi + 12*arctan(2) - 3*arctan(12/5) + 6*sqrt(3) * arctan(5/sqrt(3)) + 6*sqrt(3) * arctanh((2*sqrt(3))/5) + log(9261))/72.
%e A386732 0.000044394388389732931619793708861045902941185047688518...
%t A386732 Join[{0, 0, 0, 0}, RealDigits[1/72 (-4 (3 + Sqrt[3]) Pi + 3 (4 ArcTan[2] + 2 Sqrt[3] ArcTan[5/Sqrt[3]] + 2 ArcTan[4 - Sqrt[3]] + 2 ArcTan[4 + Sqrt[3]] + Log[21] - Sqrt[3] Log[5 - 2 Sqrt[3]] + Sqrt[3] Log[5 + 2 Sqrt[3]])), 10, 100][[1]]]
%t A386732 (* or *)
%t A386732 Join[{0, 0, 0, 0}, RealDigits[Integrate[1/(x^12 - 1), {x, 2, Infinity}], 10, 100][[1]]]
%t A386732 (* or *)
%t A386732 Join[{0, 0, 0, 0}, RealDigits[1/22528*Hypergeometric2F1[11/12, 1, 23/12, 1/4096], 10, 100][[1]]]
%Y A386732 Cf. A016644, A105199, A123868, A304656.
%K A386732 nonn,cons
%O A386732 0,5
%A A386732 _Jason Bard_, Jul 31 2025