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A212480 Decimal expansion of the argument of infinite power tower of i. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A088608 A176104 A011481 * A100221 A157683 A049110

Adjacent sequences:  A212477 A212478 A212479 * A212481 A212482 A212483

KEYWORD

nonn,cons,easy

AUTHOR

Stanislav Sykora, May 17 2012

STATUS

approved

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Last modified May 22 20:08 EDT 2017. Contains 286906 sequences.