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A201899
Decimal expansion of the greatest x satisfying x^2+3x+1=e^x.
4
2, 9, 9, 2, 2, 3, 4, 8, 7, 2, 0, 5, 3, 9, 3, 6, 8, 6, 5, 0, 9, 3, 3, 1, 1, 4, 5, 2, 7, 8, 3, 8, 8, 2, 6, 2, 1, 8, 1, 1, 5, 9, 4, 5, 4, 7, 7, 4, 9, 0, 0, 6, 3, 6, 3, 9, 1, 2, 5, 6, 2, 3, 9, 9, 9, 3, 6, 1, 6, 8, 9, 8, 5, 4, 9, 6, 4, 7, 1, 9, 5, 1, 2, 1, 1, 4, 9, 4, 4, 6, 8, 2, 5, 6, 7, 1, 0, 5, 1
OFFSET
1,1
COMMENTS
See A201741 for a guide to related sequences. The Mathematica program includes a graph.
EXAMPLE
least: -2.1093569955710161272316992470592578841155...
nearest to 0: -0.608989103010165494835043701926011...
greatest: 2.99223487205393686509331145278388262181...
MATHEMATICA
a = 1; b = 3; c = 2;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -3, 3.1}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -2.2, -2.1}, WorkingPrecision -> 110]
RealDigits[r] (* A201897, least *)
r = x /. FindRoot[f[x] == g[x], {x, -.7, -.6}, WorkingPrecision -> 110]
RealDigits[r] (* A201898, nearest 0 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
RealDigits[r] (* A201899 greatest *)
CROSSREFS
Cf. A201741.
Sequence in context: A201765 A160331 A019702 * A201894 A023400 A153637
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 06 2011
STATUS
approved