A201926 Decimal expansion of the greatest x satisfying x^2+4x+3=e^x.

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, 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, 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

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:  -3.024014501135293784775589627797395351659...
nearest to 0:  -0.79522661386054079889626155638871...
greatest:  3.2986275628038651802559413164923413431...

Mathematica

a = 1; b = 4; c = 3;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -3.5, 3.5}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -3.1, -3.0}, WorkingPrecision -> 110]
RealDigits[r]     (* A201924 *)
r = x /. FindRoot[f[x] == g[x], {x, -.8, -.7}, WorkingPrecision -> 110]
RealDigits[r]     (* A201925 *)
 r = x /. FindRoot[f[x] == g[x], {x, 3.2, 3.3}, WorkingPrecision -> 110]
RealDigits[r]     (* A201926 *)

Crossrefs

Cf. A201741.

Sequence in context: A118045 A276023 A268822 * A288055 A081233 A050676

Adjacent sequences: A201923 A201924 A201925 * A201927 A201928 A201929

Keyword

nonn,cons

Author

Clark Kimberling, Dec 06 2011

Status

approved