

A197384


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


2



1, 5, 4, 0, 6, 7, 5, 0, 0, 2, 9, 3, 4, 0, 1, 2, 5, 1, 0, 8, 8, 0, 4, 7, 8, 2, 3, 9, 5, 2, 2, 4, 3, 4, 3, 4, 4, 3, 8, 8, 3, 9, 4, 1, 0, 2, 0, 4, 5, 4, 5, 6, 5, 9, 8, 2, 5, 0, 3, 9, 3, 5, 7, 5, 6, 3, 9, 3, 4, 3, 1, 2, 7, 5, 8, 0, 4, 6, 1, 6, 2, 9, 3, 8, 1, 4, 7, 6, 2, 0, 9, 3, 9, 5, 9, 1, 4, 9, 0
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OFFSET

1,2


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=1..99.


EXAMPLE

x=1.54067500293401251088047823952243434438839410204...


MATHEMATICA

b = Pi/3; c = 1; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.5, 1.6}, WorkingPrecision > 200]
RealDigits[t] (* A197384 *)
Plot[{f[b*x], f[c*x]^2}, {x, 1.2, 1.9}]


CROSSREFS

Cf. A197133.
Sequence in context: A320411 A197012 A200137 * A193035 A227966 A021653
Adjacent sequences: A197381 A197382 A197383 * A197385 A197386 A197387


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Oct 14 2011


STATUS

approved



