

A197263


Decimal expansion of least x>0 having sin(3x)=(sin 5x)^2.


2



1, 3, 6, 6, 5, 1, 1, 9, 2, 1, 7, 0, 5, 7, 2, 3, 9, 4, 9, 5, 6, 9, 7, 6, 0, 1, 7, 8, 8, 5, 9, 0, 5, 4, 6, 3, 2, 0, 0, 1, 1, 3, 9, 1, 7, 6, 8, 4, 9, 0, 6, 8, 5, 9, 4, 1, 9, 0, 6, 3, 5, 2, 4, 2, 8, 8, 8, 1, 0, 7, 0, 4, 0, 2, 7, 1, 2, 5, 0, 1, 5, 4, 4, 0, 3, 2, 2, 6, 1, 8, 6, 7, 9, 1, 7, 2, 3, 5, 5, 7, 9, 7, 8, 9, 8, 9, 5, 8, 8, 7, 1
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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..110.


EXAMPLE

0.13665119217057239495697601788590546...


MATHEMATICA

b = 3; c = 5; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .1, .3}, WorkingPrecision > 100]
RealDigits[t] (* A197263 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 1}]


CROSSREFS

Cf. A197133.
Sequence in context: A247685 A185735 A339021 * A074785 A225462 A179949
Adjacent sequences: A197260 A197261 A197262 * A197264 A197265 A197266


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Oct 12 2011


EXTENSIONS

a(99) corrected and more terms from Georg Fischer, Jul 28 2021


STATUS

approved



