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 A129200 #29 Nov 21 2024 08:05:53 %S A129200 2,4,7,4,6,6,4,6,1,5,4,7,2,6,3,4,5,2,9,4,4,7,8,1,5,4,9,7,8,8,3,5,9,2, %T A129200 8,9,2,5,3,7,6,6,9,0,3,0,9,8,5,6,7,6,9,6,4,6,9,1,1,7,3,5,7,9,4,4,3,6, %U A129200 5,1,7,9,4,4,3,6,6,6,3,6,4,9,7,4,7,5,4,8,8,3,3,2,9,3,9,8,5,9,6 %N A129200 Decimal expansion of arcsinh(1/4). %C A129200 Archimedes's-like scheme: set p(0) = 1/sqrt(17), q(0) = 1/4; p(n+1) = 2*p(n)*q(n)/(p(n)+q(n)) (arithmetic mean of reciprocals, i.e., 1/p(n+1) = (1/p(n) + 1/q(n))/2), q(n+1) = sqrt(p(n+1)*q(n)) (geometric mean, i.e., log(q(n+1)) = (log(p(n+1)) + log(q(n)))/2), for n >= 0. The error of p(n) and q(n) decreases by a factor of approximately 4 each iteration, i.e., approximately 2 bits are gained by each iteration. Set r(n) = (2*q(n) + p(n))/3, the error decreases by a factor of approximately 16 for each iteration, i.e., approximately 4 bits are gained by each iteration. For a similar scheme see also A244644. - _A.H.M. Smeets_, Jul 12 2018 %H A129200 Muniru A Asiru, <a href="/A129200/b129200.txt">Table of n, a(n) for n = 0..2000</a> %H A129200 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a> %F A129200 Equals log((1 + sqrt(17))/4). - _Jianing Song_, Jul 12 2018 %e A129200 .24746646154726345294478154978835928925376690309856769646911... %t A129200 RealDigits[ArcSinh[1/4], 10, 111][[1]] (* _Robert G. Wilson v_, Jul 23 2018 *) %o A129200 (PARI) asinh(1/4) \\ _Michel Marcus_, Jul 12 2018 %o A129200 (Magma) SetDefaultRealField(RealField(100)); Argsinh(1/4); // _G. C. Greubel_, Nov 11 2018 %K A129200 nonn,cons %O A129200 0,1 %A A129200 _N. J. A. Sloane_, Jul 27 2008