A212479 Decimal expansion of the absolute value of infinite power tower of i.

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

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-François Alcover, Feb 05 2013 *)

Prog

(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

Crossrefs

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

Sequence in context: A299082 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