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A201924 Decimal expansion of the least x satisfying x^2+4x+3=e^x.

%I A201924 #9 Feb 07 2025 16:44:07
%S A201924 3,0,2,4,0,1,4,5,0,1,1,3,5,2,9,3,7,8,4,7,7,5,5,8,9,6,2,7,7,9,7,3,9,5,
%T A201924 3,5,1,6,5,9,8,2,8,2,8,7,1,3,2,9,0,7,9,1,9,8,7,5,0,3,5,5,4,8,2,6,2,3,
%U A201924 8,2,5,2,4,7,0,6,6,4,3,2,9,4,3,2,4,8,4,3,4,2,4,1,0,3,3,5,6,4,2
%N A201924 Decimal expansion of the least x satisfying x^2+4x+3=e^x.
%C A201924 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201924 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201924 least:  -3.024014501135293784775589627797395351659...
%e A201924 nearest to 0:  -0.79522661386054079889626155638871...
%e A201924 greatest:  3.2986275628038651802559413164923413431...
%t A201924 a = 1; b = 4; c = 3;
%t A201924 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201924 Plot[{f[x], g[x]}, {x, -3.5, 3.5}, {AxesOrigin -> {0, 0}}]
%t A201924 r = x /. FindRoot[f[x] == g[x], {x, -3.1, -3.0}, WorkingPrecision -> 110]
%t A201924 RealDigits[r]     (* A201924 *)
%t A201924 r = x /. FindRoot[f[x] == g[x], {x, -.8, -.7}, WorkingPrecision -> 110]
%t A201924 RealDigits[r]     (* A201925 *)
%t A201924  r = x /. FindRoot[f[x] == g[x], {x, 3.2, 3.3}, WorkingPrecision -> 110]
%t A201924 RealDigits[r]     (* A201926 *)
%Y A201924 Cf. A201741.
%K A201924 nonn,cons
%O A201924 1,1
%A A201924 _Clark Kimberling_, Dec 06 2011