cp's OEIS Frontend

A201895 Decimal expansion of the least x satisfying x^2+3x+1=e^x.

%I A201895 #8 Feb 07 2025 16:44:07
%S A201895 2,6,4,9,2,1,9,8,8,7,7,6,7,2,9,2,9,6,5,3,4,8,4,9,6,1,3,7,9,5,3,4,0,8,
%T A201895 1,5,2,7,9,6,9,5,4,5,4,5,4,9,7,2,0,5,7,6,3,0,7,4,6,5,8,0,9,0,6,1,2,5,
%U A201895 0,6,6,9,9,0,9,4,1,9,6,6,6,6,7,3,7,3,0,1,0,6,4,5,0,2,0,7,9,3,6
%N A201895 Decimal expansion of the least x satisfying x^2+3x+1=e^x.
%C A201895 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201895 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201895 least:  -2.649219887767292965348496137953408152796...
%e A201895 greatest:  2.8931164309252712203155349313495308853...
%t A201895 a = 1; b = 3; c = 1;
%t A201895 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201895 Plot[{f[x], g[x]}, {x, -4, 4}, {AxesOrigin -> {0, 0}}]
%t A201895 r = x /. FindRoot[f[x] == g[x], {x, -2.7, -2.6}, WorkingPrecision -> 110]
%t A201895 RealDigits[r]     (* A201895 *)
%t A201895 r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
%t A201895 RealDigits[r]     (* A201986 *)  (* NOTE: 3 zeros *)
%Y A201895 Cf. A201741.
%K A201895 nonn,cons
%O A201895 1,1
%A A201895 _Clark Kimberling_, Dec 06 2011