A201926 - OEIS

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

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

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

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

%N Decimal expansion of the greatest x satisfying x^2+4x+3=e^x.

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

%e least:  -3.024014501135293784775589627797395351659...

%e nearest to 0:  -0.79522661386054079889626155638871...

%e greatest:  3.2986275628038651802559413164923413431...

%t a = 1; b = 4; c = 3;

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, -3.1, -3.0}, WorkingPrecision -> 110]

%t RealDigits[r]     (* A201924 *)

%t r = x /. FindRoot[f[x] == g[x], {x, -.8, -.7}, WorkingPrecision -> 110]

%t RealDigits[r]     (* A201925 *)

%t  r = x /. FindRoot[f[x] == g[x], {x, 3.2, 3.3}, WorkingPrecision -> 110]

%t RealDigits[r]     (* A201926 *)

%Y Cf. A201741.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Dec 06 2011