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A201931 Decimal expansion of the least x satisfying x^2+5x+1=e^x.

%I A201931 #8 Feb 07 2025 16:44:07
%S A201931 4,7,9,3,0,9,5,4,5,5,1,2,7,4,9,3,5,8,9,5,6,5,6,2,1,1,0,8,5,0,4,2,0,4,
%T A201931 3,1,4,3,4,8,9,0,9,3,1,7,4,9,1,1,1,6,0,8,1,0,6,7,9,3,2,4,1,6,4,7,7,9,
%U A201931 2,7,2,5,5,7,4,3,6,2,1,1,3,1,9,9,3,3,1,8,8,1,4,2,4,1,1,4,3,6,1
%N A201931 Decimal expansion of the least x satisfying x^2+5x+1=e^x.
%C A201931 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201931 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201931 least:  -4.79309545512749358956562110850420...
%e A201931 greatest:  3.377361484197400579255025058889...
%t A201931 a = 1; b = 5; c = 1;
%t A201931 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201931 Plot[{f[x], g[x]}, {x, -5, 3.5}, {AxesOrigin -> {0, 0}}]
%t A201931 r = x /. FindRoot[f[x] == g[x], {x, -4.8, -4.7}, WorkingPrecision -> 110]
%t A201931 RealDigits[r]     (* A201931 *)
%t A201931 r = x /. FindRoot[f[x] == g[x], {x, 3.3, 3.4}, WorkingPrecision -> 110]
%t A201931 RealDigits[r]     (* A201932 *)
%Y A201931 Cf. A201741.
%K A201931 nonn,cons
%O A201931 1,1
%A A201931 _Clark Kimberling_, Dec 06 2011