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%I #28 Sep 08 2022 08:45:58
%S 1,7,6,0,8,3,9,5,5,5,8,8,0,0,2,8,0,9,0,7,5,6,6,4,9,8,9,5,6,3,8,3,7,2,
%T 7,4,8,0,7,9,8,0,4,0,9,4,3,1,8,5,0,9,9,0,4,6,4,6,3,8,8,2,2,5,0,5,3,4,
%U 2,8,4,1,6,8,7,5,4,5,4,6,5,8,1,1,9,0,4,6,3,5,1,1,5,2,6,3,0,5,9,8,4
%N Decimal expansion of sqrt(2)^sqrt(2)^sqrt(2).
%C If Schanuel's Conjecture is true, then sqrt(2)^sqrt(2)^sqrt(2) is transcendental (see Marques and Sondow 2010, p. 79).
%H G. C. Greubel, <a href="/A194348/b194348.txt">Table of n, a(n) for n = 1..10000</a>
%H S. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, Jun 23 2012, Section 1.1
%H 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>, arXiv:1010.6216 [math.NT], 2010-2011; East-West J. Math., 12 (2010), 75-84.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Schanuel's_conjecture">Schanuel's conjecture</a>
%e 1.76083955588002809075664989563837274807980409431850990464638822505342...
%t RealDigits[ Sqrt[2]^Sqrt[2]^Sqrt[2], 10, 100] // First
%o (PARI) sqrt(2)^sqrt(2)^sqrt(2) \\ _Charles R Greathouse IV_, May 14 2014
%o (PARI) (x->x^x^x)(sqrt(2)) \\ _Charles R Greathouse IV_, May 14 2014
%o (Magma) SetDefaultRealField(RealField(100)); Sqrt(2)^Sqrt(2)^Sqrt(2); // _G. C. Greubel_, Aug 19 2018
%Y Cf. A002193 (decimal expansion of sqrt(2)), A078333 (decimal expansion of sqrt(2)^sqrt(2)), A194555 (the decimal expansion of the real part of I^e^Pi).
%K nonn,cons
%O 1,2
%A _Jonathan Sondow_, Aug 28 2011
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