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A199621
Decimal expansion of x<0 satisfying 2*x+cos(x)=0.
2
4, 5, 0, 1, 8, 3, 6, 1, 1, 2, 9, 4, 8, 7, 3, 5, 7, 3, 0, 3, 6, 5, 3, 8, 6, 9, 6, 7, 6, 2, 6, 8, 1, 8, 2, 7, 3, 2, 0, 1, 3, 6, 5, 0, 1, 7, 2, 3, 0, 5, 5, 4, 3, 4, 0, 1, 5, 0, 5, 8, 4, 9, 1, 3, 6, 3, 6, 4, 1, 5, 6, 6, 9, 8, 5, 2, 2, 3, 3, 7, 9, 5, 4, 7, 4, 1, 4, 1, 3, 3, 0, 6, 9, 9, 2, 3, 1, 6, 2
OFFSET
0,1
COMMENTS
See A199597 for a guide to related sequences. The Mathematica program includes a graph.
This is the abscissa point x = 0.45018... where a parabola y=x^2+a and the curve y=sin(x) touch at exactly one point, a=0.23246557... - R. J. Mathar, Aug 27 2024
EXAMPLE
x=-0.450183611294873573036538696762681827320...
MATHEMATICA
a = 2; b = 1; c = 0;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.46, -.45}, WorkingPrecision -> 110]
RealDigits[r] (* A199621 *)
CROSSREFS
Cf. A199597.
Sequence in context: A262400 A075424 A200619 * A199390 A270914 A048837
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 08 2011
STATUS
approved