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 A194557 #16 Feb 16 2025 01:12:35 %S A194557 1,7,3,6,1,9,0,5,2,5,0,9,5,3,1,3,5,2,1,5,4,1,5,7,1,4,8,2,6,8,3,3,2,6, %T A194557 7,5,8,2,2,9,5,5,3,2,1,8,4,8,9,0,8,6,4,0,7,8,4,5,4,6,9,6,0,5,7,4,4,6, %U A194557 7,6,3,7,4,5,8,4,3,3,5,6,3,1,2,3,2,3,4,2,1,7,1,0,0,6,1,8,3,5,2,5 %N A194557 Decimal expansion of sqrt(3)^sqrt(27) = sqrt(27)^sqrt(3). %C A194557 Positive real numbers x < y with x^y = y^x are parameterized by (x,y) = ((1 + 1/t)^t,(1 + 1/t)^(t+1)) for t > 0. For example, t = 1/2 gives (x,y) = (sqrt(3),sqrt(27)). See Sondow and Marques 2010, pp. 155-157. %H A194557 J. Sondow and D. Marques, <a href="http://ami.ektf.hu/uploads/papers/finalpdf/AMI_37_from151to164.pdf">Algebraic and transcendental solutions of some exponential equations</a>, Annales Mathematicae et Informaticae, 37 (2010), 151-164. %H A194557 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a> %F A194557 -2*sqrt(3)*ProductLog(-1, -log(3)/(2*sqrt(3)))/log(3), where ProductLog is the Lambert W function, simplifies to sqrt(27). - _Jean-François Alcover_, Jun 01 2015 %e A194557 17.361905250953135215415714826833267582295532184890864078454696057446763745... %t A194557 RealDigits[ Sqrt[3]^Sqrt[27], 10, 100] // First %Y A194557 Cf. A073226 (decimal expansion of e^e), A194556 (decimal expansion of (9/4)^(27/8) = (27/8)^(9/4)). %K A194557 nonn,cons %O A194557 2,2 %A A194557 _Jonathan Sondow_, Aug 30 2011