A116186 Decimal expansion of real part of i^(i^i), that is, Re(i^(i^i)).

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, 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, 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

Offset: 0

Author

Peter C. Heinig (algorithms(AT)gmx.de), Apr 15 2007

Keywords

• nonn
• cons

Comments

If Schanuel's Conjecture is true, then i^i^i is transcendental (see Marques and Sondow 2010, p. 79).

Examples

			i^(i^i) = 0.947158998072378380653475352018 + 0.320764449979308534660116845875 i.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Steven Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020-2022, Section 1.1.
• Diego Marques and Jonathan Sondow, Schanuel's conjecture and algebraic powers z^w and w^z with z and w transcendental, arXiv:1010.6216 [math.NT], 2010-2011; East-West J. Math., 12 (2010), 75-84.
• Wikipedia, Schanuel's conjecture.

Crossrefs

Cf. A049006, A116191.

Programs

Magma

C := ComplexField(100);  Real(I^I^I); // G. C. Greubel, May 11 2019

Mathematica

RealDigits[ Re[I^I^I], 10, 100] // First

PARI

real(I^I^I) \\ Charles R Greathouse IV, May 15 2013

Sage

numerical_approx((i^i^i).real(), digits=100) # G. C. Greubel, May 11 2019

Formula

Equals cos(Pi/2 * e^(-Pi/2)). - David Ulgenes, Feb 08 2024