A140663 - OEIS

%I #9 Jul 13 2015 21:08:15

%S 2,0,7,1,9,6,9,2,2,9,0,8,2,3,1,2,9,1,5,2,3,4,1,9,0,5,5,6,3,6,3,2,9,5,

%T 7,7,7,8,5,3,5,3,3,8,0,7,5,9,5,4,1,1,6,2,2,7,1,7,4,9,0,8,1,8,3,9,4,6,

%U 6,6,1,0,9,8,5,2,7,7,3,4,0,0,6,9,0,0,6,6,5,7,7,5,4,6,3,0,9,8,5,3,8,5,4,6,2

%N Decimal expansion of the number x defined by x^(x^x) = 27.

%e 2.07196922908231...

%p Digits := 120: x := 2.071 : for i from 1 to 30 do xxx := x^(x^x) : n := xxx-27 : d := xxx*(x^x*log(x)*(1+log(x))+x^(x-1)) ; x := evalf(x-n/d) ; print(x) ; od: # _R. J. Mathar_, Aug 08 2008

%t digits = 105; x0 = x /. FindRoot[x^(x^x) == 27, {x, 2}, WorkingPrecision -> digits+1]; RealDigits[x0, 10, digits][[1]] (* _Jean-François Alcover_, Jan 28 2014 *)

%Y Cf. A093590.

%K cons,nonn

%O 1,1

%A _Joshua Taylor_, Jul 11 2008

%E Extended beyond 15 digits by _R. J. Mathar_, Aug 08 2008