A197387 Decimal expansion of least x > 0 having sin(Pi*x/3) = sin(x/2)^2.

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

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..98.

Example

x=2.15321506668269833543390122784461348429261632049...

Mathematica

b = Pi/3; c = 1/2; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 2, 2.5}, WorkingPrecision -> 200]
RealDigits[t] (* A197387 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 3}]

Crossrefs

Cf. A197133.

Sequence in context: A188392 A356558 A143409 * A171177 A171176 A332529

Adjacent sequences: A197384 A197385 A197386 * A197388 A197389 A197390

Keyword

nonn,cons

Author

Clark Kimberling, Oct 14 2011

Extensions

Incorrect term a(99) removed by Andrew Howroyd, Jan 17 2018

Status

approved