

A197394


Decimal expansion of least x>0 having sin(pi*x/4)=(sin x/3)^2.


2



2, 9, 9, 8, 8, 7, 3, 7, 3, 2, 3, 3, 1, 8, 9, 8, 6, 2, 1, 7, 7, 6, 8, 5, 1, 9, 0, 3, 1, 3, 9, 1, 6, 1, 0, 2, 1, 9, 0, 2, 4, 5, 5, 2, 2, 8, 6, 7, 3, 2, 7, 1, 9, 5, 4, 0, 2, 6, 0, 1, 4, 1, 6, 1, 9, 5, 0, 6, 8, 4, 6, 1, 8, 6, 6, 1, 4, 4, 9, 9, 7, 3, 2, 2, 8, 5, 1, 0, 3, 2, 9, 6, 2, 7, 6, 4, 0, 3, 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=2.998873732331898621776851903139161021...


MATHEMATICA

b = Pi/4; c = 1/3; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 2.95, 3.0}, WorkingPrecision > 200]
RealDigits[t](* A197394 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 3.1}]


CROSSREFS

Cf. A197133.
Sequence in context: A266274 A003678 A201683 * A198942 A168333 A238412
Adjacent sequences: A197391 A197392 A197393 * A197395 A197396 A197397


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Oct 14 2011


STATUS

approved



