A197418 Decimal expansion of least x > 0 having sin(Pi*x/6) = sin(2*x/3)^2.

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

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.

Example

x=1.4959095464399948574965751863169680911...

Mathematica

b = Pi/6; c = 2/3; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.49, 1.5}, WorkingPrecision -> 200]
RealDigits[t] (* A197418 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 3}]

Crossrefs

Cf. A197133.

Sequence in context: A243710 A242610 A292484 * A137807 A163103 A019688

Adjacent sequences: A197415 A197416 A197417 * A197419 A197420 A197421

Keyword

nonn,cons

Author

Clark Kimberling, Oct 14 2011

Status

approved