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A201907
Decimal expansion of the greatest x satisfying x^2+4x+2=e^x.
4
3, 2, 3, 4, 9, 2, 3, 2, 1, 7, 7, 7, 6, 0, 6, 6, 3, 6, 7, 0, 3, 2, 7, 9, 6, 1, 3, 2, 7, 3, 0, 4, 4, 3, 0, 4, 4, 8, 4, 7, 8, 6, 8, 0, 4, 6, 8, 7, 0, 4, 0, 9, 6, 1, 1, 3, 1, 4, 6, 8, 8, 5, 5, 3, 1, 4, 3, 8, 6, 6, 5, 2, 1, 0, 2, 5, 9, 3, 6, 4, 2, 2, 0, 9, 5, 3, 8, 2, 5, 6, 0, 8, 1, 5, 7, 5, 9, 8, 1
OFFSET
1,1
COMMENTS
See A201741 for a guide to related sequences. The Mathematica program includes a graph.
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: A086035 A334449 A268289 * A003559 A200599 A239947
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 06 2011
STATUS
approved