A201745 Decimal expansion of the number x satisfying x^2+6=e^x.

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

Offset

1,1

Comments

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

Links

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

Index entries for transcendental numbers.

Example

2.50933666802503632454641026786985273842....

Mathematica

a = 1; b = 0; c = 6;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 2.5, 2.6}, WorkingPrecision -> 110]
RealDigits[r]    (* A201745 *)

Prog

(PARI) solve(x=2, 3, x^2+6-exp(x)) \\ Charles R Greathouse IV, Nov 26 2024

Crossrefs

Cf. A201741.

Sequence in context: A349353 A111466 A308715 * A192042 A214119 A088307

Adjacent sequences: A201742 A201743 A201744 * A201746 A201747 A201748

Keyword

nonn,cons

Author

Clark Kimberling, Dec 05 2011

Status

approved