

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
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OFFSET

0,1


COMMENTS

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


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000
S. Finch, Errata and Addenda to Mathematical Constants, Jun 23 2012, Section 1.1
Steven R. Finch, Errata and Addenda to Mathematical Constants, January 22, 2016. [Cached copy, with permission of the author]
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], 20102011; EastWest J. Math., 12 (2010), 7584.
Wikipedia, Schanuel's conjecture


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: A128751 A129168 A293416 * A024578 A030327 A095890
Adjacent sequences: A194552 A194553 A194554 * A194556 A194557 A194558


KEYWORD

nonn,cons


AUTHOR

Jonathan Sondow, Aug 28 2011


STATUS

approved



