A197385 Decimal expansion of least x > 0 having sin(Pi*x/3) = sin(2*x)^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

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.

Index entries for transcendental numbers.

Example

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}]

Prog

(PARI) solve(x=.2, .3, sin(x*Pi/3)-sin(2*x)^2) \\ Charles R Greathouse IV, Jul 22 2026

Crossrefs

Cf. A197133.

Sequence in context: A388151 A011288 A198234 * A010596 A359699 A131920

Adjacent sequences: A197382 A197383 A197384 * A197386 A197387 A197388

Keyword

nonn,cons,changed

Author

Clark Kimberling, Oct 14 2011

Status

approved