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A201905 Decimal expansion of the least x satisfying x^2+4x+2=e^x. 4
3, 4, 2, 5, 6, 6, 7, 4, 1, 0, 2, 0, 2, 8, 7, 7, 3, 7, 3, 2, 6, 5, 6, 2, 6, 0, 6, 4, 7, 2, 5, 8, 1, 6, 6, 9, 7, 8, 2, 7, 3, 5, 7, 2, 6, 1, 7, 3, 3, 2, 3, 3, 5, 5, 5, 3, 6, 6, 6, 3, 4, 3, 8, 0, 6, 5, 1, 2, 9, 4, 4, 3, 4, 9, 4, 2, 4, 4, 2, 7, 5, 0, 1, 2, 8, 7, 3, 9, 9, 6, 5, 9, 7, 0, 2, 5, 7, 7, 1 (list; constant; graph; refs; listen; history; text; internal format)
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:  -3.425667410202877373265626064725816697827357...

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: A209688 A143939 A197269 * A138609 A322466 A211377

Adjacent sequences:  A201902 A201903 A201904 * A201906 A201907 A201908

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Dec 06 2011

STATUS

approved

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Last modified June 30 03:34 EDT 2022. Contains 354913 sequences. (Running on oeis4.)