A201935 - OEIS

%I #5 Mar 30 2012 18:58:03

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

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

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

%N Decimal expansion of the greatest x satisfying x^2+5x+2=e^x.

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

%e least:  -4.5640783603793772013414868523420...

%e nearest to 0:  -0.259069533051109108686405...

%e greatest:  3.43200871161068035280379146269...

%t a = 1; b = 5; c = 2;

%t f[x_] := a*x^2 + b*x + c; g[x_] := E^x

%t Plot[{f[x], g[x]}, {x, -5, 3.5}, {AxesOrigin -> {0, 0}}]

%t  r = x /. FindRoot[f[x] == g[x], {x, -4.6, -4.5}, WorkingPrecision -> 110]

%t RealDigits[r]     (* A201933 *)

%t  r = x /. FindRoot[f[x] == g[x], {x, -.3, -.2}, WorkingPrecision -> 110]

%t RealDigits[r]     (* A201934 *)

%t  r = x /. FindRoot[f[x] == g[x], {x, 3.4, 3.5}, WorkingPrecision -> 110]

%t RealDigits[r]     (* A201935 *)

%Y Cf. A201741.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Dec 06 2011