A201907 - OEIS

%I #8 Feb 07 2025 16:44:07

%S 3,2,3,4,9,2,3,2,1,7,7,7,6,0,6,6,3,6,7,0,3,2,7,9,6,1,3,2,7,3,0,4,4,3,

%T 0,4,4,8,4,7,8,6,8,0,4,6,8,7,0,4,0,9,6,1,1,3,1,4,6,8,8,5,5,3,1,4,3,8,

%U 6,6,5,2,1,0,2,5,9,3,6,4,2,2,0,9,5,3,8,2,5,6,0,8,1,5,7,5,9,8,1

%N Decimal expansion of the greatest x satisfying x^2+4x+2=e^x.

%C See A201741 for a guide to related sequences. The Mathematica program includes a graph.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%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 1,1

%A _Clark Kimberling_, Dec 06 2011