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 A072112 #20 Jun 22 2021 12:28:14
%S A072112 3,2,8,6,7,4,1,6,2,9,0,8,5,4,6,2,1,6,8,1,8,2,8,4,5,1,4,0,4,3,1,1,5,1,
%T A072112 1,8,9,7,6,9,4,1,5,4,7,6,5,5,7,8,1,9,0,9,6,1,5,5,1,3,3,2,3,9,0,9,5,7,
%U A072112 0,5,1,5,9,6,9,6,5,7,1,2,5,5,0,2,2,1,8,2,2,6,1,8,9,1,5,6,8,8,9,3,1,9,1,8
%N A072112 Decimal expansion of Hall and Tenenbaum constant.
%C A072112 For any multiplicative function g with values -1<= g(k) <= 1, for any real x >=2, Sum( i<= x, g(i) ) << x * exp{ -K * Sum( p<=x, (1-g(p))/p ) } and K is the optimal constant satisfying this inequality (Hall and Tenenbaum, 1991).
%C A072112 Named after the British mathematician Richard Roxby Hall and the French mathematician Gérald Tenenbaum (b. 1952). - _Amiram Eldar_, Jun 22 2021
%D A072112 G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, p. 348, Publications de l'Institut Cartan, 1990.
%H A072112 R. R. Hall and G. Tenenbaum, <a href="https://doi.org/10.1017/S0305004100070419">Effective mean value estimates for complex multiplicative functions</a>, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 110, No. 2 (1991), pp. 337-351.
%F A072112 K = cos(S) = 0.3286... where S is the root 0 < S < 2*Pi of sin(S)+(Pi-S)*cos(S) = Pi/2.
%e A072112 0.32867416290854621681828451404311511897694154765578...
%t A072112 digits = 104; x /. FindRoot[Pi*x + Sqrt[1 - x^2] - x*ArcCos[x] == Pi/2, {x, 0}, WorkingPrecision -> digits] // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Feb 15 2013 *)
%o A072112 (PARI) \p 200;
%o A072112 cos(solve(X=0,2*Pi,sin(X)+(Pi-X)*cos(X)-Pi/2))
%Y A072112 Cf. A072113.
%K A072112 cons,easy,nonn
%O A072112 0,1
%A A072112 _Benoit Cloitre_, Jun 19 2002