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A201772 Decimal expansion of the number x satisfying x^2+x+4=e^x.

%I A201772 #9 Feb 07 2025 16:44:07
%S A201772 2,5,8,5,5,5,4,6,3,3,7,1,1,7,3,7,7,9,5,6,2,4,6,8,6,3,6,3,0,2,7,8,0,6,
%T A201772 7,7,3,2,3,0,8,3,3,3,0,0,0,0,1,7,5,4,9,2,6,0,5,2,1,4,0,3,5,9,1,1,2,8,
%U A201772 2,4,2,8,7,0,2,2,1,9,0,7,6,1,4,0,1,3,8,0,9,7,5,8,6,7,0,3,6,2,6
%N A201772 Decimal expansion of the number x satisfying x^2+x+4=e^x.
%C A201772 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201772 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201772 2.58555463371173779562468636302780677323083330000...
%t A201772 a = 1; b = 1; c = 4;
%t A201772 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201772 Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
%t A201772 r = x /. FindRoot[f[x] == g[x], {x, 2.5, 2.6}, WorkingPrecision -> 110]
%t A201772 RealDigits[r]     (* A201772 *)
%Y A201772 Cf. A201741.
%K A201772 nonn,cons
%O A201772 1,1
%A A201772 _Clark Kimberling_, Dec 06 2011