A194554 Decimal expansion of the absolute value of the imaginary part of i^(e^Pi), where i = sqrt(-1).

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, 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, 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

Offset: 0

Author

Jonathan Sondow, Aug 28 2011

Keywords

• nonn
• cons

Comments

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

Examples

			i^e^Pi = 0.2192048949... - 0.9756788478...*i
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Steven Finch, Errata and Addenda to Mathematical Constants, Jun 23 2012, Section 1.1
• D. Marques and Jonathan Sondow, Schanuel's conjecture and algebraic powers z^w and w^z with z and w transcendental, https://arxiv.org/abs/1010.6216 [math.NT], 2010-2011; East-West J. Math., 12 (2010), 75-84.
• Wikipedia, Schanuel's conjecture

Crossrefs

Cf. A039661 (decimal expansion of e^Pi), A194555 (real part).

Programs

Mathematica

RealDigits[Im[I^E^Pi], 10, 100] // First

PARI

abs(imag(I^(exp(Pi)))) \\ Michel Marcus, Aug 19 2018