A212480 - OEIS

%I #15 Aug 08 2014 01:40:33

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

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

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

%N Decimal expansion of the argument of infinite power tower of i.

%C This c, expressed in radians, equals arg(z), where z is the complex solution of z = i^z or, equivalently, z = i^i^i^... Also, c = atan(A077590/A077589).

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

%F c = arg(i^i^i^...).

%e 0.6884532271077021304987675711768242596 ...

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

%o (PARI) \\ start with I^(0.4+0.4*I) and iterate (%+I^%)/2. It converges pretty rapidly to z.

%Y Cf. A077589 (real part of z), A077590 (imaginary part of z), A212479 (absolute value of z).

%K nonn,cons,easy

%O 0,1

%A _Stanislav Sykora_, May 17 2012