A212480 Decimal expansion of the argument of infinite power tower of i.

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, 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, 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

Offset

0,1

Comments

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).

Links

Table of n, a(n) for n=0..107.

Eric Weisstein's World of Mathematics, Power Tower

Formula

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

Example

0.6884532271077021304987675711768242596 ...

Mathematica

2*I*ProductLog[-I*Pi/2]/Pi // Arg // N[#, 108]& // RealDigits[#][[1]]& (* Jean-François Alcover, Feb 05 2013 *)

Prog

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

Crossrefs

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

Sequence in context: A323984 A176104 A011481 * A100221 A157683 A300897

Adjacent sequences: A212477 A212478 A212479 * A212481 A212482 A212483

Keyword

nonn,cons,easy

Author

Stanislav Sykora, May 17 2012

Status

approved