cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A116191 Decimal expansion of imaginary part of i^(i^i), that is, Im(i^(i^i)).

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%I A116191 #30 Oct 23 2024 11:38:31
%S A116191 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,
%T A116191 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,
%U A116191 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
%N A116191 Decimal expansion of imaginary part of i^(i^i), that is, Im(i^(i^i)).
%C A116191 If Schanuel's Conjecture is true, then i^i^i is transcendental (see Marques and Sondow 2010, p. 79).
%H A116191 G. C. Greubel, <a href="/A116191/b116191.txt">Table of n, a(n) for n = 0..10000</a>
%H A116191 Nicholas John Bizzell-Browning, <a href="https://bura.brunel.ac.uk/handle/2438/29960">LIE scales: Composing with scales of linear intervallic expansion</a>, Ph. D. Thesis, Brunel Univ. (UK, 2024). See p. 144.
%H A116191 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, Jun 23 2012, Section 1.1
%H A116191 D. Marques and J. Sondow, <a href="http://arxiv.org/abs/1010.6216">Schanuel's conjecture and algebraic powers z^w and w^z with z and w transcendental</a>,  East-West J. Math., 12 (2010), 75-84.
%H A116191 Wikipedia, <a href="http://en.wikipedia.org/wiki/Schanuel&#39;s_conjecture">Schanuel's conjecture</a>
%F A116191 Equals sin((Pi/2)/exp(Pi/2)). - _Peter Luschny_, Oct 23 2024
%e A116191 i^(i^i) = 0.947158998072378380653475352018 + 0.320764449979308534660116845875 i.
%p A116191 c := sin((Pi/2)/exp(Pi/2)): Digits := 110: evalf(c, Digits)*10^105:
%p A116191 ListTools:-Reverse(convert(floor(%), base, 10));  # _Peter Luschny_, Oct 23 2024
%t A116191 RealDigits[ Im[I^I^I], 10, 100] // First
%o A116191 (PARI) imag(I^I^I) \\ _Charles R Greathouse IV_, May 15 2013
%o A116191 (Magma) C<I> := ComplexField(100);  Im(I^I^I); // _G. C. Greubel_, May 11 2019
%o A116191 (Sage) numerical_approx((i^i^i).imag(), digits=100) # _G. C. Greubel_, May 11 2019
%Y A116191 Cf. A049006, A116186.
%K A116191 nonn,cons
%O A116191 0,1
%A A116191 Peter C. Heinig (algorithms(AT)gmx.de), Apr 15 2007