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A200682
Decimal expansion of the greater of two values of x satisfying 3*x^2 = tan(x) and 0 < x < Pi/2.
3
1, 4, 0, 3, 0, 6, 0, 4, 2, 0, 8, 0, 9, 3, 7, 1, 2, 3, 8, 8, 4, 8, 9, 2, 1, 3, 4, 9, 4, 4, 9, 4, 4, 2, 0, 1, 5, 7, 1, 2, 9, 3, 1, 3, 8, 4, 2, 4, 5, 1, 1, 1, 4, 6, 8, 9, 5, 9, 4, 8, 8, 5, 9, 1, 8, 5, 2, 9, 0, 1, 7, 3, 9, 6, 5, 1, 5, 1, 1, 0, 2, 5, 2, 8, 1, 8, 7, 6, 3, 1, 0, 6, 4, 1, 3, 8, 5, 0, 6
OFFSET
1,2
COMMENTS
See A200614 for a guide to related sequences. The Mathematica program includes a graph.
EXAMPLE
lesser: 0.34742576447743871128905641295532587...
greater: 1.40306042080937123884892134944944201...
MATHEMATICA
a = 3; c = 0;
f[x_] := a*x^2 - c; g[x_] := Tan[x]
Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .3, .4}, WorkingPrecision -> 110]
RealDigits[r] (* A200681 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r] (* A200682 *)
CROSSREFS
Cf. A200614.
Sequence in context: A281653 A327305 A290328 * A263618 A156788 A130801
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 20 2011
STATUS
approved