login
A116191
Decimal expansion of imaginary part of i^(i^i), that is, Im(i^(i^i)).
2
3, 2, 0, 7, 6, 4, 4, 4, 9, 9, 7, 9, 3, 0, 8, 5, 3, 4, 6, 6, 0, 1, 1, 6, 8, 4, 5, 8, 7, 4, 8, 6, 3, 1, 4, 0, 1, 0, 2, 3, 6, 7, 0, 2, 0, 6, 8, 1, 2, 7, 6, 7, 9, 9, 8, 2, 9, 6, 5, 7, 1, 6, 8, 7, 4, 0, 7, 5, 5, 2, 2, 2, 1, 5, 9, 3, 6, 3, 0, 0, 1, 8, 1, 3, 0, 8, 6, 3, 3, 9, 7, 2, 7, 5, 2, 7, 5, 9, 5, 6, 5, 1, 7, 9, 7
OFFSET
0,1
COMMENTS
If Schanuel's Conjecture is true, then i^i^i is transcendental (see Marques and Sondow 2010, p. 79).
LINKS
Nicholas John Bizzell-Browning, LIE scales: Composing with scales of linear intervallic expansion, Ph. D. Thesis, Brunel Univ. (UK, 2024). See p. 144.
Steven R. Finch, Errata and Addenda to Mathematical Constants, Jun 23 2012, Section 1.1
D. Marques and J. Sondow, Schanuel's conjecture and algebraic powers z^w and w^z with z and w transcendental, East-West J. Math., 12 (2010), 75-84.
FORMULA
Equals sin((Pi/2)/exp(Pi/2)). - Peter Luschny, Oct 23 2024
EXAMPLE
i^(i^i) = 0.947158998072378380653475352018 + 0.320764449979308534660116845875 i.
MAPLE
c := sin((Pi/2)/exp(Pi/2)): Digits := 110: evalf(c, Digits)*10^105:
ListTools:-Reverse(convert(floor(%), base, 10)); # Peter Luschny, Oct 23 2024
MATHEMATICA
RealDigits[ Im[I^I^I], 10, 100] // First
PROG
(PARI) imag(I^I^I) \\ Charles R Greathouse IV, May 15 2013
(Magma) C<I> := ComplexField(100); Im(I^I^I); // G. C. Greubel, May 11 2019
(Sage) numerical_approx((i^i^i).imag(), digits=100) # G. C. Greubel, May 11 2019
CROSSREFS
Sequence in context: A010604 A067585 A173787 * A257303 A048199 A335998
KEYWORD
nonn,cons,changed
AUTHOR
Peter C. Heinig (algorithms(AT)gmx.de), Apr 15 2007
STATUS
approved