A201905 Decimal expansion of the least x satisfying x^2+4x+2=e^x.

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

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.

Example

least:  -3.425667410202877373265626064725816697827357...
nearest to 0:  -0.35687491913863648565066705875991244...
greatest:  3.2349232177760663670327961327304430448478...

Mathematica

a = 1; b = 4; c = 2;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -4, 3.3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -3.5, -3.4}, WorkingPrecision -> 110]
RealDigits[r]     (* A201905 *)
r = x /. FindRoot[f[x] == g[x], {x, -.36, -.35}, WorkingPrecision -> 110]
RealDigits[r]     (* A201906 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.2, 3.3}, WorkingPrecision -> 110]
RealDigits[r]     (* A201907 *)

Crossrefs

Cf. A201741.

Sequence in context: A209688 A143939 A197269 * A138609 A322466 A211377

Adjacent sequences: A201902 A201903 A201904 * A201906 A201907 A201908

Keyword

nonn,cons

Author

Clark Kimberling, Dec 06 2011

Status

approved