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A201933 Decimal expansion of the least x satisfying x^2 + 5*x + 2 = e^x.

%I A201933 #13 Feb 07 2025 16:44:07
%S A201933 4,5,6,4,0,7,8,3,6,0,3,7,9,3,7,7,2,0,1,3,4,1,4,8,6,8,5,2,3,4,2,0,7,4,
%T A201933 4,8,0,6,9,5,7,9,6,4,3,4,6,1,3,1,4,1,1,1,2,5,2,3,5,7,5,3,5,9,5,4,2,6,
%U A201933 0,2,8,0,7,3,3,7,5,3,7,0,3,7,9,6,6,5,8,2,3,8,8,1,9,7,7,1,3,8,2
%N A201933 Decimal expansion of the least x satisfying x^2 + 5*x + 2 = e^x.
%C A201933 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201933 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201933 least:  -4.5640783603793772013414868523420...
%e A201933 nearest to 0:  -0.259069533051109108686405...
%e A201933 greatest:  3.43200871161068035280379146269...
%t A201933 a = 1; b = 5; c = 2;
%t A201933 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201933 Plot[{f[x], g[x]}, {x, -5, 3.5}, {AxesOrigin -> {0, 0}}]
%t A201933 r = x /. FindRoot[f[x] == g[x], {x, -4.6, -4.5}, WorkingPrecision -> 110]
%t A201933 RealDigits[r]     (* A201933 *)
%t A201933 r = x /. FindRoot[f[x] == g[x], {x, -.3, -.2}, WorkingPrecision -> 110]
%t A201933 RealDigits[r]     (* A201934 *)
%t A201933 r = x /. FindRoot[f[x] == g[x], {x, 3.4, 3.5}, WorkingPrecision -> 110]
%t A201933 RealDigits[r]     (* A201935 *)
%Y A201933 Cf. A201741.
%K A201933 nonn,cons
%O A201933 1,1
%A A201933 _Clark Kimberling_, Dec 06 2011
%E A201933 a(87) onwards corrected by _Georg Fischer_, Aug 03 2021