This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A332324 #8 Mar 06 2020 23:02:47
%S A332324 2,7,0,3,9,4,7,6,5,2,0,5,1,8,4,6,0,7,9,6,2,4,5,9,6,1,3,3,8,3,1,1,0,9,
%T A332324 1,1,9,6,1,4,6,0,2,1,2,8,1,4,2,8,3,3,3,6,2,3,2,5,6,7,9,9,4,1,0,6,3,8,
%U A332324 1,5,9,0,9,7,8,9,9,1,0,3,8,0,4,5,8,0
%N A332324 Decimal expansion of the minimum value of the 4th Maclaurin polynomial of e^x.
%C A332324 Let p(n,x) denote the n-th Maclaurin polynomial of e^x, and let p'(n,x) denote its derivative. Then p'(n+1,x) = p(n,x), so that the real zero of p(n,x), for odd n, is also the value of x that minimizes p(n+1,x). See A117605 for the (negated) real zero p(3,x).
%e A332324 Minimum value = 0.2703947652051846079624596133831109119614602128142...
%t A332324 z = 150; p[n_, x_] := Normal[Series[E^x, {x, 0, n}]];
%t A332324 t = x /. NSolve[p[3, x] == 0, x, z][[1]]
%t A332324 RealDigits[t][[1]]
%t A332324 Plot[Evaluate[p[4, x]], {x, -3, 1}, PlotRange -> {-1, 3}]
%Y A332324 Cf. A117605.
%K A332324 nonn,cons,easy
%O A332324 0,1
%A A332324 _Clark Kimberling_, Feb 11 2020