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

Author

Stanislav Sykora, May 17 2012

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			0.5675551633069578253846131441924533439 ...
		

Links

• Eric Weisstein's World of Mathematics, Power Tower

Crossrefs

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

Programs

Mathematica

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

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

Formula

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