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A201904 Decimal expansion of the greatest x satisfying x^2+4x+1=e^x.

%I A201904 #8 Feb 07 2025 16:44:07
%S A201904 3,1,6,4,1,3,7,1,1,1,6,3,7,9,3,8,3,2,5,2,8,4,4,6,6,9,6,6,7,3,8,9,2,1,
%T A201904 5,9,6,5,6,1,5,5,3,9,9,2,8,5,9,5,4,4,6,8,2,9,4,2,9,6,9,5,3,8,4,1,0,1,
%U A201904 9,5,2,1,7,6,4,7,0,9,8,9,5,4,3,6,1,5,6,7,8,3,8,2,0,9,3,2,1,8,6
%N A201904 Decimal expansion of the greatest x satisfying x^2+4x+1=e^x.
%C A201904 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201904 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201904 least:  -3.73890200966899672518020580953927823014766...
%e A201904 greatest:  3.164137111637938325284466966738921596561...
%t A201904 a = 1; b = 4; c = 1;
%t A201904 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201904 Plot[{f[x], g[x]}, {x, -4, 3.3}, {AxesOrigin -> {0, 0}}]
%t A201904 r = x /. FindRoot[f[x] == g[x], {x, -3.8, -3.7}, WorkingPrecision -> 110]
%t A201904 RealDigits[r]     (* A201903 *)
%t A201904  r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.2}, WorkingPrecision -> 110]
%t A201904 RealDigits[r]     (* A201904 *)
%Y A201904 Cf. A201741.
%K A201904 nonn,cons
%O A201904 1,1
%A A201904 _Clark Kimberling_, Dec 06 2011