

A197376


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


1



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

1,1


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=1..99.


EXAMPLE

x=2.2142974355881810060341309203570740...


MATHEMATICA

b = 1; c = 1/2; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 2, 2.5}, WorkingPrecision > 200]
RealDigits[t] (* *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 2.5}]
RealDigits[ 2*ArcCos[ 1/Sqrt[5] ], 10, 99] // First (* JeanFrançois Alcover, Feb 19 2013 *)


CROSSREFS

Cf. A197133.
Sequence in context: A191320 A180228 A212320 * A113072 A328025 A305326
Adjacent sequences: A197373 A197374 A197375 * A197377 A197378 A197379


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Oct 14 2011


STATUS

approved



