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%I #7 Aug 03 2021 13:55:54
%S 3,5,6,8,7,4,9,1,9,1,3,8,6,3,6,4,8,5,6,5,0,6,6,7,0,5,8,7,5,9,9,1,2,4,
%T 4,0,9,5,9,9,2,0,0,5,2,6,2,0,8,0,4,2,0,9,9,6,8,1,8,4,5,7,7,9,2,0,7,4,
%U 7,0,6,1,9,1,8,6,6,5,3,2,2,5,4,6,3,2,9,0,5,7,9,7,6,8,9,3,3,7,2,8
%N Decimal expansion of the x nearest 0 that satisfies x^2 + 4*x + 2 = e^x.
%C See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%e least: -3.425667410202877373265626064725816697827357...
%e nearest to 0: -0.35687491913863648565066705875991244...
%e greatest: 3.2349232177760663670327961327304430448478...
%t a = 1; b = 4; c = 2;
%t f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t Plot[{f[x], g[x]}, {x, -4, 3.3}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -3.5, -3.4}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201905 *)
%t r = x /. FindRoot[f[x] == g[x], {x, -.36, -.35}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201906 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 3.2, 3.3}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201907 *)
%Y Cf. A201741.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Dec 06 2011
%E a(84) onwards corrected by _Georg Fischer_, Aug 03 2021
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