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 A377813 #21 Dec 01 2024 11:37:51 %S A377813 7,2,1,8,1,7,7,3,7,5,8,9,4,0,5,1,7,1,2,4,6,6,3,8,3,7,0,1,3,6,5,5,2,6, %T A377813 3,4,7,0,2,7,7,6,5,0,1,5,7,8,4,9,0,7,7,9,4,9,1,5,2,7,2,5,3,2,6,0,2,4, %U A377813 5,8,0,1,4,1,2,3,3 %N A377813 Decimal expansion of arctanh(phi-1). %C A377813 arctanh(phi-1) is the solution for real valued x in tanh(x) = d/dx tanh(x). %C A377813 arctanh(phi-1) is the solution for real valued x in cosh(x) * sinh(x) = 1. - _Colin Linzer_, Nov 22 2024 %H A377813 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a> %F A377813 Equals (1/2)*log(2+sqrt(5)). %F A377813 Equals (3/2)*log(phi). %F A377813 Equals arccosh(sqrt(phi)). %F A377813 Equals arcsinh(sqrt(phi-1)). %F A377813 Equals f(phi-1) with f(x) = (1/2)*log((2-x+2*sqrt(1-x))/x), a branch of the converse function of the derivative of tanh(x). %F A377813 Equals 3*A202541. - _Hugo Pfoertner_, Nov 12 2024 %F A377813 Equals arcsinh(2)/2. - _Colin Linzer_, Nov 22 2024 %e A377813 0.721817737589405171246638370136552634702... %t A377813 RealDigits[ArcTanh[GoldenRatio - 1], 10, 120][[1]] (* _Amiram Eldar_, Nov 12 2024 *) %o A377813 (PARI) atanh((1+sqrt(5))/2-1) %Y A377813 Cf. A001622, A202541. %K A377813 nonn,cons %O A377813 0,1 %A A377813 _Colin Linzer_, Nov 08 2024