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A116191
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Decimal expansion of imaginary part of i^(i^i), that is, Im(i^(i^i)).
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2
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3, 2, 0, 7, 6, 4, 4, 4, 9, 9, 7, 9, 3, 0, 8, 5, 3, 4, 6, 6, 0, 1, 1, 6, 8, 4, 5, 8, 7, 4, 8, 6, 3, 1, 4, 0, 1, 0, 2, 3, 6, 7, 0, 2, 0, 6, 8, 1, 2, 7, 6, 7, 9, 9, 8, 2, 9, 6, 5, 7, 1, 6, 8, 7, 4, 0, 7, 5, 5, 2, 2, 2, 1, 5, 9, 3, 6, 3, 0, 0, 1, 8, 1, 3, 0, 8, 6, 3, 3, 9, 7, 2, 7, 5, 2, 7, 5, 9, 5, 6, 5, 1, 7, 9, 7
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OFFSET
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0,1
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COMMENTS
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If Schanuel's Conjecture is true, then i^i^i is transcendental (see Marques and Sondow 2010, p. 79).
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LINKS
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EXAMPLE
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i^(i^i) = 0.947158998072378380653475352018 + 0.320764449979308534660116845875 i.
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MATHEMATICA
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RealDigits[ Im[I^I^I], 10, 100] // First
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PROG
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(Magma) C<I> := ComplexField(100); Im(I^I^I) // G. C. Greubel, May 11 2019
(Sage) numerical_approx((i^i^i).imag(), digits=100) # G. C. Greubel, May 11 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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Peter C. Heinig (algorithms(AT)gmx.de), Apr 15 2007
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STATUS
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approved
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