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A194554
Decimal expansion of the absolute value of the imaginary part of i^(e^Pi), where i = sqrt(-1).
2
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
0,1
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, https://arxiv.org/abs/1010.6216, 201-2011; East-West J. Math., 12 (2010), 75-84.
EXAMPLE
i^e^Pi = 0.2192048949... - 0.9756788478...*i
MATHEMATICA
RealDigits[Im[I^E^Pi], 10, 100] // First
PROG
(PARI) abs(imag(I^(exp(Pi)))) \\ Michel Marcus, Aug 19 2018
CROSSREFS
Cf. A039661 (decimal expansion of e^Pi), A194555 (real part).
Sequence in context: A188141 A244667 A307235 * A065467 A021839 A349009
KEYWORD
nonn,cons
AUTHOR
Jonathan Sondow, Aug 28 2011
STATUS
approved