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 A194624 #10 May 14 2019 21:40:26
%S A194624 1,5,3,5,1,6,7,8,9,6,6,3,9,5,2,9,4,7,1,5,0,0,6,8,3,3,2,9,7,8,4,6,3,2,
%T A194624 2,7,7,1,1,2,6,9,4,8,5,4,8,9,9,6,9,6,2,0,3,1,7,9,8,5,4,2,8,3,3,4,3,7,
%U A194624 2,6,1,3,6,4,1,9,0,5,8,3,0,2,9,3,6,8,7,6,6,0,5,3,0,1,9,3,7,1,9,4
%N A194624 Decimal expansion of the smaller solution to x^x = 3/4.
%C A194624 Since (1/e)^(1/e) < 3/4 < 1, the equation x^x = 3/4 has two solutions x = a and x = b with 0 < a < 1/e < b < 1. Both solutions are transcendental (see Proposition 2.2 in Sondow-Marques 2010).
%H A194624 J. Sondow and D. 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.
%H A194624 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e A194624 0.15351678966395294715006833297846322771126948548996962031798542833437261364190...
%t A194624 x = x /. FindRoot[x^x == 3/4, {x, 0.1}, WorkingPrecision -> 120]; RealDigits[x, 10, 100] // First
%Y A194624 Cf. A030798 (x^x = 2), A072364 ((1/e)^(1/e)), A194625 (larger solution to x^x = 3/4).
%K A194624 nonn,cons
%O A194624 0,2
%A A194624 _Jonathan Sondow_, Sep 02 2011