Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #30 Dec 15 2024 12:12:12
%S 9,7,5,6,7,8,8,4,7,8,0,3,6,6,9,3,8,5,6,4,3,4,6,8,9,6,6,0,5,5,4,2,3,1,
%T 1,0,5,2,2,9,4,6,9,7,1,6,4,8,1,0,8,5,3,7,6,8,8,7,2,0,2,6,5,0,3,7,8,0,
%U 6,6,8,4,2,2,9,8,4,5,8,4,4,2,7,9,4,9,0,8,2,6,2,6,7,2,7,4,4,1,3,2
%N Decimal expansion of the absolute value of the imaginary part of i^(e^Pi), where i = sqrt(-1).
%C If Schanuel's Conjecture is true, then i^e^Pi is transcendental (see Marques and Sondow 2010, p. 79).
%H G. C. Greubel, <a href="/A194554/b194554.txt">Table of n, a(n) for n = 0..10000</a>
%H Steven Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, Jun 23 2012, Section 1.1
%H D. Marques and Jonathan 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>, https://arxiv.org/abs/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>
%e i^e^Pi = 0.2192048949... - 0.9756788478...*i
%t RealDigits[Im[I^E^Pi], 10, 100] // First
%o (PARI) abs(imag(I^(exp(Pi)))) \\ _Michel Marcus_, Aug 19 2018
%Y Cf. A039661 (decimal expansion of e^Pi), A194555 (real part).
%K nonn,cons
%O 0,1
%A _Jonathan Sondow_, Aug 28 2011