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

0,1

Comments

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

References

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

Links

Table of n, a(n) for n=0..100.

Eric Weisstein's World of Mathematics, i.

Eric Weisstein's World of Mathematics, Power Tower.

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

Example

0.43828293672703211162697516355126482426789735164639460360922124049579153222269568...

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]

Prog

(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
(PARI) real(lambertw(-I*Pi/2)*2*I/Pi) \\ Charles R Greathouse IV, Sep 26 2025

Crossrefs

Cf. A049006, A077590 (imaginary part).

Sequence in context: A099289 A231892 A065628 * A114941 A161016 A019835

Adjacent sequences: A077586 A077587 A077588 * A077590 A077591 A077592

Keyword

nonn,cons,nice

Author

Eric W. Weisstein, Nov 07 2002

Status

approved