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 A258500 #13 Dec 07 2024 18:39:09
%S A258500 7,4,0,8,7,6,4,6,8,6,9,6,5,7,7,4,5,2,1,9,5,7,2,9,5,0,2,8,5,1,0,6,1,4,
%T A258500 3,8,9,8,0,4,1,7,1,1,4,1,0,7,4,0,0,0,1,5,1,8,2,2,7,1,8,3,9,3,7,9,1,7,
%U A258500 0,7,1,7,1,0,0,1,3,8,4,0,2,2,8,4,2,1,8,2,3,1,1,9,2,3,0,4,7,0,6,6,7
%N A258500 Decimal expansion of the nontrivial real solution of x^(3/2) = (3/2)^x.
%H A258500 Jonathan Sondow, Diego Marques, <a href="http://arxiv.org/abs/1108.6096">Algebraic and transcendental solutions of some exponential equations</a>, Annales Mathematicae et Informaticae 37 (2010) 151-164.
%F A258500 x0 = -((x*ProductLog(-1, -(log(x)/x)))/log(x)), with x = 3/2, where ProductLog is the Lambert W function.
%e A258500 x0 = 7.408764686965774521957295028510614389804171141074...
%e A258500 z = x0^(3/2) = 20.16595073003535058942970947434890012034363496 ...
%e A258500 z > e^e = 15.15426224... = A073226.
%t A258500 x0 = -((x*ProductLog[-1, -(Log[x]/x)])/Log[x]) /. x -> 3/2; RealDigits[x0, 10, 101] // First
%t A258500 RealDigits[x/.FindRoot[x^(3/2)==(3/2)^x,{x,7},WorkingPrecision->120],10,120][[1]] (* _Harvey P. Dale_, Dec 07 2024 *)
%Y A258500 Cf. A073226, A194556, A194557, A258501 (x^(5/2)=(5/2)^x), A258502 (x^(7/2)=(7/2)^x).
%K A258500 nonn,cons,easy
%O A258500 1,1
%A A258500 _Jean-François Alcover_, Jun 01 2015