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%I #49 Jul 02 2023 14:27:27
%S 1,4,7,6,6,8,4,3,3,7,3,5,7,8,6,9,9,4,7,0,8,9,2,3,5,5,8,5,3,7,3,8,8,9,
%T 8,3,8,6,5,5,1,6,8,9,3,0,9,8,5,5,2,6,9,8,4,4,6,4,4,0,3,1,4,7,6,2,1,6,
%U 9,8,0,0,2,9,1,8,8,2,1,5,2,8,5,9,7,1,4,7,2,4,0,8,4,4,0,2,6,9,5,7,9,8,3,2,2
%N Decimal expansion of the positive root of x^x^x = 2.
%C As follows from Gelfond's theorem, the root is irrational, so this sequence is infinite and aperiodic. Its transcendence is, apparently, still an open problem. - _Vladimir Reshetnikov_, Apr 27 2013
%H Ash J. Marshall and Yiren Tan, <a href="http://condor.depaul.edu/mash/atotheamg.pdf">A rational number of the form a^a with a irrational</a>, Mathematical Gazette 96, March 2012, pp. 106-109.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GelfondsTheorem.html">Gelfond's Theorem</a>
%e 1.4766843373578699470892355853738898386551689309855269844644...
%t First[RealDigits[Root[{Function[x, x^x^x - 2], 1.477`4}], 10, 100]]
%o (PARI) solve(x=1,2,x^x^x-2) \\ _Charles R Greathouse IV_, Apr 14 2014
%Y Cf. A030798.
%K nonn,cons,easy
%O 1,2
%A _Vladimir Reshetnikov_, Nov 07 2011
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