A077589 Decimal expansion of real part of the infinite power tower of i.

4, 3, 8, 2, 8, 2, 9, 3, 6, 7, 2, 7, 0, 3, 2, 1, 1, 1, 6, 2, 6, 9, 7, 5, 1, 6, 3, 5, 5, 1, 2, 6, 4, 8, 2, 4, 2, 6, 7, 8, 9, 7, 3, 5, 1, 6, 4, 6, 3, 9, 4, 6, 0, 3, 6, 0, 9, 2, 2, 1, 2, 4, 0, 4, 9, 5, 7, 9, 1, 5, 3, 2, 2, 2, 2, 6, 9, 5, 6, 8, 7, 6, 6, 9, 1, 7, 2, 1, 4, 0, 5, 3, 8, 2, 0, 4, 0, 7, 5, 4, 9

Offset: 0

Author

Eric W. Weisstein, Nov 07 2002

Keywords

• nonn
• cons
• nice

Comments

This is the real part of i^i^i^i^i^i...

Examples

			0.43828293672703211162697516355126482426789735164639460360922124049579153222269568...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 6.11, p. 449.

Links

• Eric Weisstein's World of Mathematics, i.
• Eric Weisstein's World of Mathematics, Power Tower.

Crossrefs

Cf. A049006, A077590 (imaginary part).

Programs

Maple

evalf(Re(2*I*LambertW(-I*Pi/2)/Pi), 137);  # Alois P. Heinz, Dec 12 2023

Mathematica

Prepend@@RealDigits[Re[ -ProductLog[ -Log[I]]/Log[I]], 10, 150]

PARI

z=(1+I)/2;e=.1^default(realprecision);until(e>abs(z-z-=(z-I^z)/(1-I^(z+1)*Pi/2)),);digits(real(z)\e) \\ M. F. Hasler, May 17 2018

Formula

The value is 2 (i/Pi) W(-i Pi/2) = 0.4382829... + i 0.360592..., where W denotes the principal branch of the Lambert W function. - David W. Cantrell, Nov 23 2007