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%I #16 Mar 18 2024 06:01:29
%S 1,2,5,3,4,9,8,7,5,5,6,9,9,9,5,3,4,7,1,6,4,3,3,6,0,9,3,7,9,0,5,7,9,8,
%T 9,4,0,3,6,9,2,3,2,2,0,8,3,3,2,0,1,3,4,1,7,0,6,3,8,3,4,7,1,6,6,4,0,9,
%U 5,2,4,8,2,0,4,8,9,8,7,1,7,0,8,9,0,2,4
%N Decimal expansion of Sum_{k>=2} 1/(k! - 1).
%C Erdős was interested in the question whether this constant is 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 Paul Erdős, <a href="https://www.renyi.hu/~p_erdos/1988-22.pdf">On the irrationality of certain series: problems and results</a>, in Alan Baker (ed.), New Advances in Transcendence Theory, Cambridge University Press, 1988, p. 102.
%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 1.25349875569995347164336093790579894036923220833201...
%t RealDigits[Sum[1/(k! - 1), {k, 2, 300}], 10, 100][[1]]
%o (PARI) suminf(k=2, 1/(k!-1)) \\ _Michel Marcus_, May 03 2020
%Y Cf. A033312, A331372, A327826.
%K nonn,cons
%O 1,2
%A _Amiram Eldar_, May 03 2020
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