%I #26 May 12 2023 09:08:57

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

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

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

%N Decimal expansion of the absolute value of infinite power tower of i.

%C This c = |z|, where z is the complex solution of z = i^z or, equivalently, z = i^i^i^...

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PowerTower.html">Power Tower</a>

%F c = |i^i^i^...|.

%e 0.5675551633069578253846131441924533439 ...

%t 2*I*ProductLog[-I*Pi/2]/Pi // Abs // N[#, 108]& // RealDigits[#][[1]]& (* _Jean-François Alcover_, Feb 05 2013 *)

%o (PARI) my(z="I"); for (i=1, 1000, z = concat(z, "^I")); z = eval(z); sqrt(norml2([real(z), imag(z)])) \\ _Michel Marcus_, May 12 2023

%Y Cf. A077589 (real part of z), A077590 (imaginary part of z), A212480 (argument of z).

%K nonn,cons,easy

%O 0,1

%A _Stanislav Sykora_, May 17 2012