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A212479 Decimal expansion of the absolute value of infinite power tower of i. 1
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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

LINKS

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

Eric Weisstein's World of Mathematics, Power Tower

FORMULA

c = |i^i^i^...|.

EXAMPLE

0.5675551633069578253846131441924533439 ...

MATHEMATICA

2*I*ProductLog[-I*Pi/2]/Pi // Abs // N[#, 108]& // RealDigits[#][[1]]& (* Jean-Fran├žois Alcover, Feb 05 2013 *)

PROG

PARI/GP: 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), A212480 (argument of z).

Sequence in context: A021642 A171423 A101288 * A095942 A139395 A029911

Adjacent sequences:  A212476 A212477 A212478 * A212480 A212481 A212482

KEYWORD

nonn,cons,easy

AUTHOR

Stanislav Sykora, May 17 2012

STATUS

approved

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Last modified April 30 12:40 EDT 2017. Contains 285669 sequences.