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A197415 Decimal expansion of least x>0 having sin(pi*x/6)=(sin 3x)^2. 2
0, 5, 8, 7, 7, 5, 0, 5, 6, 2, 2, 4, 6, 2, 9, 9, 5, 0, 9, 7, 7, 6, 4, 4, 1, 4, 2, 2, 4, 2, 5, 9, 4, 8, 4, 2, 4, 0, 9, 2, 7, 7, 4, 9, 0, 1, 9, 2, 7, 3, 1, 7, 9, 3, 6, 4, 3, 0, 6, 4, 7, 4, 3, 2, 6, 6, 6, 5, 3, 6, 9, 2, 4, 4, 8, 5, 1, 6, 4, 0, 7, 6, 4, 5, 9, 9, 9, 1, 5, 3, 3, 0, 2, 2, 3, 7, 5, 0, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The Mathematica program includes a graph.  See A197133 for a guide to least x>0 satisfying sin(b*x)=(sin(c*x))^2 for selected b and c.

LINKS

Table of n, a(n) for n=0..98.

EXAMPLE

x=0.0587750562246299509776441422425948...

MATHEMATICA

b = Pi/6; c = 3; f[x_] := Sin[x]

t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 0.05, 0.06},

   WorkingPrecision -> 200]

RealDigits[t] (* A197415 *)

Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.2}]

CROSSREFS

Cf. A197133.

Sequence in context: A165909 A243598 A230366 * A019845 A143618 A177056

Adjacent sequences:  A197412 A197413 A197414 * A197416 A197417 A197418

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 14 2011

STATUS

approved

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Last modified February 23 14:19 EST 2020. Contains 332160 sequences. (Running on oeis4.)