A077590 - OEIS

A077590

Decimal expansion of imaginary part of the infinite power tower of i.

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,1

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.

EXAMPLE

0.36059247187138548595294052690600065382657703078602700474145129838046019521150773...

MAPLE

evalf(Im(2*I*LambertW(-I*Pi/2)/Pi), 139); # Alois P. Heinz, Dec 12 2023

MATHEMATICA

Prepend@@RealDigits[Im[ -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(imag(z)\e) \\ M. F. Hasler, May 17 2018