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A201935 Decimal expansion of the greatest x satisfying x^2+5x+2=e^x.

%I A201935 #8 Feb 07 2025 16:44:07
%S A201935 3,4,3,2,0,0,8,7,1,1,6,1,0,6,8,0,3,5,2,8,0,3,7,9,1,4,6,2,6,9,4,7,1,9,
%T A201935 7,0,6,0,4,2,2,3,3,0,3,7,3,5,4,2,0,5,2,1,0,0,8,7,1,4,8,9,9,5,3,7,4,7,
%U A201935 9,7,1,1,3,4,3,6,4,6,3,1,4,1,6,5,3,4,9,1,1,4,0,0,4,6,5,3,3,1,8
%N A201935 Decimal expansion of the greatest x satisfying x^2+5x+2=e^x.
%C A201935 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201935 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201935 least:  -4.5640783603793772013414868523420...
%e A201935 nearest to 0:  -0.259069533051109108686405...
%e A201935 greatest:  3.43200871161068035280379146269...
%t A201935 a = 1; b = 5; c = 2;
%t A201935 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201935 Plot[{f[x], g[x]}, {x, -5, 3.5}, {AxesOrigin -> {0, 0}}]
%t A201935  r = x /. FindRoot[f[x] == g[x], {x, -4.6, -4.5}, WorkingPrecision -> 110]
%t A201935 RealDigits[r]     (* A201933 *)
%t A201935  r = x /. FindRoot[f[x] == g[x], {x, -.3, -.2}, WorkingPrecision -> 110]
%t A201935 RealDigits[r]     (* A201934 *)
%t A201935  r = x /. FindRoot[f[x] == g[x], {x, 3.4, 3.5}, WorkingPrecision -> 110]
%t A201935 RealDigits[r]     (* A201935 *)
%Y A201935 Cf. A201741.
%K A201935 nonn,cons
%O A201935 1,1
%A A201935 _Clark Kimberling_, Dec 06 2011