login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A201896
Decimal expansion of the greatest x satisfying x^2 + 3*x + 1 = e^x.
2
2, 8, 9, 3, 1, 1, 6, 4, 3, 0, 9, 2, 5, 2, 7, 1, 2, 2, 0, 3, 1, 5, 5, 3, 4, 9, 3, 1, 3, 4, 9, 5, 3, 0, 8, 8, 5, 3, 0, 4, 0, 7, 9, 0, 9, 1, 5, 4, 6, 9, 7, 7, 4, 0, 1, 8, 2, 1, 6, 3, 4, 9, 2, 8, 1, 6, 6, 5, 5, 3, 6, 6, 0, 7, 8, 3, 3, 7, 3, 0, 5, 1, 9, 0, 8, 9, 2, 1, 0, 2, 3, 8, 8, 7, 1, 7, 3, 4, 9
OFFSET
1,1
COMMENTS
See A201741 for a guide to related sequences. The Mathematica program includes a graph.
EXAMPLE
least: -2.649219887767292965348496137953408152796...
greatest: 2.8931164309252712203155349313495308853...
MATHEMATICA
a = 1; b = 3; c = 1;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -4, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -2.7, -2.6}, WorkingPrecision -> 110]
RealDigits[r] (* A201895 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
RealDigits[r] (* A201896 *) (* NOTE 3 zeros *)
CROSSREFS
Cf. A201741.
Sequence in context: A316138 A011062 A155922 * A374644 A154859 A179377
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 06 2011
EXTENSIONS
a(98) onwards corrected by Georg Fischer, Aug 03 2021
STATUS
approved