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A201926 Decimal expansion of the greatest x satisfying x^2+4x+3=e^x.

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