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%I #7 Jan 14 2023 13:27:56
%S 1,1,2,5,0,3,0,5,1,7,5,7,8,1,2,5,0,0,0,1,0,8,4,2,0,2,1,7,2,4,8,5,5,0,
%T 4,4,3,4,0,0,7,4,5,2,8,0,0,8,6,9,9,4,1,7,1,1,4,2,5,7,8,1,2,5,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,1,7,2,7,2,3,3,7,1,1,0,1,8,8,8,8,9,2,5,0,7,7,2
%N Decimal expansion of Sum_{k>=0} 1/(2^(2^(2*k)) - 1).
%C This constant is transcendental (Schwarz, 1967).
%H Wolfgang Schwarz, <a href="https://www.jstor.org/stable/24489854">Remarks on the irrationality and transcendence of certain series</a>, Mathematica Scandinavica, Vol. 20, No. 2 (1967), pp. 269-274; <a href="https://www.mscand.dk/article/download/10836/8857">alternative link</a>.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals A076214 - A346190.
%e 1.12503051757812500010842021724855044340074528008699...
%t RealDigits[Sum[1/(2^(2^(2*n) - 1)), {n, 0, 10}], 10, 100][[1]]
%Y Cf. A048649, A076214, A346190, A346192.
%K nonn,cons
%O 1,3
%A _Amiram Eldar_, Jul 09 2021