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A201932 Decimal expansion of the greatest x satisfying x^2+5x+1=e^x.

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