A201937 Decimal expansion of the greatest negative number x satisfying 2*x^2=e^(-x).

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

Offset

1,2

Comments

See A201936 for a guide to related sequences. The Mathematica program includes a graph.

Links

Table of n, a(n) for n=1..99.

Example

least x:  -2.617866613066812769178978059143202...
greatest negative x:  -1.487962065498177156254...
greatest x:  0.5398352769028200492118039083633...

Mathematica

a = 2; b = 0; c = 0;
f[x_] := a*x^2 + b*x + c; g[x_] := E^-x
Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -3, -2}, WorkingPrecision -> 110]
RealDigits[r]  (* A201936 *)
r = x /. FindRoot[f[x] == g[x], {x, -2, -1}, WorkingPrecision -> 110]
RealDigits[r]   (* A201937 *)
r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
RealDigits[r]   (* A201938 *)

Crossrefs

Cf. A201936.

Sequence in context: A021209 A247605 A244000 * A211456 A309665 A196205

Adjacent sequences: A201934 A201935 A201936 * A201938 A201939 A201940

Keyword

nonn,cons

Author

Clark Kimberling, Dec 13 2011

Status

approved