

A197385


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


2



2, 8, 8, 4, 4, 9, 4, 1, 6, 5, 1, 2, 4, 6, 1, 5, 2, 8, 8, 3, 7, 9, 4, 6, 3, 5, 9, 5, 7, 1, 3, 8, 7, 1, 6, 3, 9, 1, 5, 1, 7, 5, 0, 8, 6, 6, 9, 3, 6, 1, 0, 8, 8, 2, 2, 5, 7, 3, 4, 3, 5, 7, 8, 7, 1, 6, 2, 4, 8, 9, 9, 2, 1, 4, 3, 4, 8, 7, 3, 8, 4, 5, 7, 2, 3, 6, 3, 2, 1, 8, 0, 0, 2, 2, 6, 7, 0, 7, 4
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


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=0.2884494165124615288379463595713871639151750...


MATHEMATICA

b = Pi/3; c = 2; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 0.2, 0.4}, WorkingPrecision > 200]
RealDigits[t] (* A197385 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 1.2}]


CROSSREFS

Cf. A197133.
Sequence in context: A242168 A011288 A198234 * A010596 A131920 A180308
Adjacent sequences: A197382 A197383 A197384 * A197386 A197387 A197388


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Oct 14 2011


STATUS

approved



