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A077589 Decimal expansion of real part of the infinite power tower of i. 9
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

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

0.43828293672703211162697516355126482426789735164639460360922124049579153222269569...

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

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

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Last modified September 25 21:12 EDT 2018. Contains 315425 sequences. (Running on oeis4.)