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A201903 Decimal expansion of the least x satisfying x^2+4x+1=e^x.

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