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A201896
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Decimal expansion of the greatest x satisfying x^2 + 3*x + 1 = e^x.
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1
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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
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OFFSET
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1,1
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COMMENTS
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See A201741 for a guide to related sequences. The Mathematica program includes a graph.
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LINKS
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EXAMPLE
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least: -2.649219887767292965348496137953408152796...
greatest: 2.8931164309252712203155349313495308853...
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MATHEMATICA
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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]
r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
RealDigits[r] (* A201986 *) (* NOTE 3 zeros *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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