login
A197257
Decimal expansion of least x>0 having sin(2x)=(sin 6x)^2.
2
0, 5, 7, 7, 0, 1, 1, 3, 3, 6, 9, 3, 5, 6, 3, 9, 4, 1, 4, 2, 9, 6, 1, 8, 3, 7, 3, 9, 7, 8, 6, 8, 4, 3, 5, 2, 4, 2, 0, 1, 7, 7, 1, 0, 9, 8, 8, 9, 9, 1, 0, 0, 9, 5, 1, 6, 6, 9, 5, 5, 8, 9, 3, 4, 1, 2, 1, 4, 3, 4, 6, 1, 2, 1, 1, 9, 4, 7, 3, 0, 8, 8, 6, 5, 2, 4, 3, 1, 5, 7, 3, 0, 6, 4, 2, 1, 7, 2, 7, 8, 0
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.
EXAMPLE
x=0.0577011336935639414296183739786...
MATHEMATICA
b = 2; c = 6; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .05, .07}, WorkingPrecision -> 100]
RealDigits[t] (* A197257 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/4}]
CROSSREFS
Cf. A197133.
Sequence in context: A217678 A227452 A138306 * A217175 A338558 A173930
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 12 2011
EXTENSIONS
a(100) corrected by Sean A. Irvine, Sep 08 2021
STATUS
approved