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A201907 Decimal expansion of the greatest x satisfying x^2+4x+2=e^x.

%I A201907 #8 Feb 07 2025 16:44:07
%S A201907 3,2,3,4,9,2,3,2,1,7,7,7,6,0,6,6,3,6,7,0,3,2,7,9,6,1,3,2,7,3,0,4,4,3,
%T A201907 0,4,4,8,4,7,8,6,8,0,4,6,8,7,0,4,0,9,6,1,1,3,1,4,6,8,8,5,5,3,1,4,3,8,
%U A201907 6,6,5,2,1,0,2,5,9,3,6,4,2,2,0,9,5,3,8,2,5,6,0,8,1,5,7,5,9,8,1
%N A201907 Decimal expansion of the greatest x satisfying x^2+4x+2=e^x.
%C A201907 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201907 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201907 least:  -3.425667410202877373265626064725816697827357...
%e A201907 nearest to 0:  -0.35687491913863648565066705875991244...
%e A201907 greatest:  3.2349232177760663670327961327304430448478...
%t A201907 a = 1; b = 4; c = 2;
%t A201907 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201907 Plot[{f[x], g[x]}, {x, -4, 3.3}, {AxesOrigin -> {0, 0}}]
%t A201907 r = x /. FindRoot[f[x] == g[x], {x, -3.5, -3.4}, WorkingPrecision -> 110]
%t A201907 RealDigits[r]     (* A201905 *)
%t A201907 r = x /. FindRoot[f[x] == g[x], {x, -.36, -.35}, WorkingPrecision -> 110]
%t A201907 RealDigits[r]     (* A201906 *)
%t A201907  r = x /. FindRoot[f[x] == g[x], {x, 3.2, 3.3}, WorkingPrecision -> 110]
%t A201907 RealDigits[r]     (* A201907 *)
%Y A201907 Cf. A201741.
%K A201907 nonn,cons
%O A201907 1,1
%A A201907 _Clark Kimberling_, Dec 06 2011