%I #17 May 04 2020 09:32:22
%S 3,4,3,6,7,3,4,3,3,1,8,1,7,6,9,0,1,8,5,4,4,4,8,2,8,3,3,3,8,1,2,4,1,2,
%T 0,6,1,8,8,8,0,7,1,7,6,4,8,6,7,8,3,8,4,8,6,5,1,1,0,5,9,2,1,7,4,5,5,0,
%U 0,9,5,4,1,2,4,1,8,0,9,7,4,9,5,2,6,7,8
%N Decimal expansion of Sum_{k>=1} 1/(2^k - 3).
%C Erdős and Graham (1980) asked whether this constant is irrational, and Borwein (1991) proved that it is indeed irrational.
%D Paul Erdős, Some of my favourite unsolved problems, in A. Baker, B. Bollobás and A. Hajnal (eds.), A tribute to Paul Erdős, Cambridge University Press, 1990, p. 470.
%H Peter B. Borwein, <a href="https://doi.org/10.1016/S0022-314X(05)80041-1">On the irrationality of Sigma (1/(q^n + r))</a>, Journal of Number Theory, Vol. 37, No. 3 (1991), pp. 253-259.
%H Paul Erdős and Ronald L. Graham, <a href="http://www.math.ucsd.edu/~fan/ron/papers/80_11_number_theory.pdf">Old and new problems and results in combinatorial number theory</a>, L'enseignement Mathématique, Université de Genève, 1980, p. 62.
%e 0.34367343318176901854448283338124120618880717648678...
%t RealDigits[Sum[1/(2^k - 3), {k, 1, 400}], 10, 100][[1]]
%o (PARI) suminf(k=1, 1/(2^k - 3)) \\ _Michel Marcus_, May 03 2020
%Y Cf. A036563 (2^n-3), A065442.
%K nonn,cons
%O 0,1
%A _Amiram Eldar_, May 03 2020
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