%I #11 Mar 10 2020 17:52:13
%S 5,9,7,4,9,5,3,9,2,5,6,6,4,3,3,6,2,3,8,7,4,7,1,3,9,5,8,8,2,5,0,7,3,8,
%T 9,9,4,0,8,3,4,1,5,1,7,3,2,6,8,1,5,3,3,5,6,4,6,6,4,5,3,0,0,5,5,6,8,1,
%U 3,9,8,1,3,8,8,5,0,7,8,2,2,3,2,1,5,5,3,2,1,8,5,5,1,5,1,6,4,2,0,0,5,6,9,4
%N Decimal expansion of constant C > 0 such that Sum_{k>=1} C^k! = 1.
%F C = 0.5974953925664336... .
%t digits = 105; Clear[f];
%t f[m_] := f[m] = Module[{s}, s[c_?NumericQ] := NSum[c^k!, {k, 1, m}, WorkingPrecision -> digits]; c /. FindRoot[s[c] == 1, {c, 1/2}, WorkingPrecision -> digits] // RealDigits // First];
%t f[1]; f[m = 2];
%t While[f[m] != f[m/2], m = 2 m; Print["m = ", m]];
%t f[m] (* _Jean-François Alcover_, Mar 10 2020 *)
%K cons,nonn
%O 0,1
%A _Benoit Cloitre_, Jan 12 2003
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