A306654 - OEIS

%I #14 Mar 15 2019 22:48:36

%S 1,4,6,5,7,8,8,8,0,0,6,7,5,7,2,4,3,6,9,8,1,9,3,7,8,3,9,5,7,5,4,5,9,3,

%T 4,0,9,8,9,7,5,4,0,6,8,9,9,0,8,8,0,9,0,2,3,7,7,7,0,5,4,1,5,8,7,2,5,4,3

%N Decimal expansion of least zero of Sum_{k>=1} 1/(k! - x).

%C The first 4 zeros: 1.465... < 4.437... < 18.594... < 97.130...; if z(n) is the n-th zero, then n! < z(n) < (n+1)!.

%e Least zero = 1.4657888006757243698...

%t f[x_] := Sum[1/(n! - x), {n, 1, 30}]

%t Plot[f[x], {x, 0, 2}]

%t x  /. NSolve[f[x] == 0, x, 10, WorkingPrecision -> 50]

%t FindRoot[f[x], {x, 1.46579}, WorkingPrecision -> 50]

%t f[1.465788800675724369]

%Y Cf. A324330.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Mar 03 2019