A201760 - OEIS

%I #7 Jun 26 2022 04:58:06

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

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

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

%N Decimal expansion of the greatest x satisfying -x^2+6 = e^x.

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

%e least:  -2.431479659723036039736539014083415082...

%e greatest:  1.3977805354241768741646854746062333...

%t a = -1; b = 0; c = 6;

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

%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -2.5, -2.4}, WorkingPrecision -> 110]

%t RealDigits[r]     (* A201759 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A201760 *)

%Y Cf. A201741.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Dec 05 2011