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A194555
Decimal expansion of the real part of i^(e^Pi), where i = sqrt(-1).
4
2, 1, 9, 2, 0, 4, 8, 9, 4, 9, 0, 0, 8, 7, 6, 1, 3, 2, 8, 9, 0, 7, 6, 7, 9, 4, 9, 7, 4, 4, 6, 5, 7, 2, 6, 5, 8, 7, 3, 6, 9, 2, 6, 4, 6, 1, 1, 9, 0, 7, 9, 6, 3, 9, 2, 6, 4, 8, 5, 0, 9, 2, 1, 7, 3, 8, 9, 3, 1, 7, 0, 7, 6, 5, 2, 1, 9, 9, 7, 4, 7, 2, 2, 3, 5, 3, 0, 1, 9, 5, 4, 0, 6, 1, 5, 3, 4, 6, 1, 0
OFFSET
0,1
COMMENTS
If Schanuel's Conjecture is true, then i^e^Pi is transcendental (see Marques and Sondow 2010, p. 79).
LINKS
S. 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, arXiv:1010.6216 [math.NT], 2010-2011; East-West J. Math., 12 (2010), 75-84.
EXAMPLE
i^e^Pi = 0.2192048949... - 0.9756788478...*i
MATHEMATICA
RealDigits[ Re[I^E^Pi], 10, 100] // First
PROG
(PARI) real(I^(exp(Pi))) \\ Michel Marcus, Aug 19 2018
CROSSREFS
Cf. A039661 (e^Pi), A194554 (imaginary part).
Cf. A194348 (sqrt(2)^(sqrt(2)^sqrt(2))).
Sequence in context: A360733 A353204 A293416 * A024578 A030327 A095890
KEYWORD
nonn,cons
AUTHOR
Jonathan Sondow, Aug 28 2011
STATUS
approved