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%I #16 Aug 24 2023 04:52:42
%S 6,5,4,0,4,0,8,6,0,0,4,2,0,6,9,4,7,1,9,8,2,2,2,8,2,9,0,0,5,3,3,9,3,1,
%T 4,5,8,0,8,6,6,7,5,9,3,4,3,5,6,5,3,8,9,7,5,6,3,7,0,3,7,5,3,8,8,0,0,3,
%U 2,5,8,3,0,5,5,0,0,1,8,9,3,9,4,8,7,7,0,0,1,6,7,5,8,7,6,1,5,5,2,8,3,4,9,8,6,2,7,2,8,2,0,8,8,2,8,4,2,2,6,3,9,8,8,1,7,6,7,0,6,5,8,8,4,1,8,3,2,0,6,3,6,9,3,7,4,2,8,8,3,4,4,4,0,2,9,9,3,4,4,3,2,0,7,2,9,1,6,9,6,9,8,8,7,0,0,7,8,6,4,4,0,0,5,3,5,8,0,0,0,2,0,1,2,6,5,6,8,5,5,3
%N Decimal expansion of (1/2)^(1/2)^(1/2)^(1/2).
%C A weak form of Schanuel's Conjecture implies that (1/2)^(1/2)^(1/2)^(1/2) is transcendental--see Marques and Sondow (2012).
%H D. Marques and J. Sondow, <a href="http://arxiv.org/abs/1212.6931">The Schanuel Subset Conjecture implies Gelfond's Power Tower Conjecture</a>, arXiv:1212.6931 [math.NT], 2012-2013.
%e 0.6540408600420694719822282900533931458086675934356538975637037538800325830550...
%t RealDigits[ (1/2)^(1/2)^(1/2)^(1/2), 10, 200] [[1]]
%Y Cf. A220782.
%K nonn,cons
%O 0,1
%A _Jonathan Sondow_, Dec 31 2012