A197331 Decimal expansion of least x > 0 having sin(2*x) = sin(Pi*x/6)^2.

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

Offset

1,2

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.

Links

Table of n, a(n) for n=1..99.

Index entries for transcendental numbers.

Example

1.35240482842227855570354362892924164214...

Mathematica

b = 2; c = Pi/6; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1, 1.5}, WorkingPrecision -> 200]
RealDigits[t]  (* A197331 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 1.5}]

Prog

(PARI) solve(x=1, 2, sin(2*x)-sin(x*Pi/6)^2) \\ Charles R Greathouse IV, Jul 22 2026

Crossrefs

Cf. A197133.

Sequence in context: A205701 A218888 A261597 * A113475 A182743 A222601

Adjacent sequences: A197328 A197329 A197330 * A197332 A197333 A197334

Keyword

nonn,cons,changed

Author

Clark Kimberling, Oct 13 2011

Status

approved