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%I #28 Feb 08 2024 13:37:55
%S 9,4,7,1,5,8,9,9,8,0,7,2,3,7,8,3,8,0,6,5,3,4,7,5,3,5,2,0,1,8,1,9,3,3,
%T 3,3,5,0,3,9,0,6,1,3,3,9,0,3,1,4,9,3,6,3,6,7,1,3,6,8,1,1,7,9,4,4,6,9,
%U 2,9,2,7,9,3,0,0,4,8,8,0,8,4,5,2,6,2,6,2,6,8,4,6,2,6,4,9,0,2,2,3,7,4,9,5,3
%N Decimal expansion of real part of i^(i^i), that is, Re(i^(i^i)).
%C If Schanuel's Conjecture is true, then i^i^i is transcendental (see Marques and Sondow 2010, p. 79).
%H G. C. Greubel, <a href="/A116186/b116186.txt">Table of n, a(n) for n = 0..10000</a>
%H S. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, arXiv:2001.00578 [math.HO], 2020-2022, Section 1.1
%H D. Marques and J. Sondow, <a href="http://arxiv.org/abs/1010.6216">Schanuel's conjecture and algebraic powers z^w and w^z with z and w transcendental</a>, arXiv:1010.6216 [math.NT], 2010-2011; East-West J. Math., 12 (2010), 75-84.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Schanuel's_conjecture">Schanuel's conjecture</a>
%F Equals cos(Pi/2 * e^(-Pi/2)). - _David Ulgenes_, Feb 08 2024
%e i^(i^i) = 0.947158998072378380653475352018 + 0.320764449979308534660116845875 i.
%t RealDigits[ Re[I^I^I], 10, 100] // First
%o (PARI) real(I^I^I) \\ _Charles R Greathouse IV_, May 15 2013
%o (Magma) C<I> := ComplexField(100); Real(I^I^I) // _G. C. Greubel_, May 11 2019
%o (Sage) numerical_approx((i^i^i).real(), digits=100) # _G. C. Greubel_, May 11 2019
%Y Cf. A049006, A116191.
%K nonn,cons
%O 0,1
%A Peter C. Heinig (algorithms(AT)gmx.de), Apr 15 2007
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