A197285 Decimal expansion of least x>0 having sin(5x)=(sin 3x)^2.

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

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..100.

Example

x=0.40978000673394594139576877636550397172589211...

Mathematica

b = 5; c = 3; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .4, .7}, WorkingPrecision -> 100]
RealDigits[t]  (* A197285 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/2}]

Crossrefs

Cf. A197133.

Sequence in context: A269720 A245638 A176220 * A357017 A352672 A188147

Adjacent sequences: A197282 A197283 A197284 * A197286 A197287 A197288

Keyword

nonn,cons

Author

Clark Kimberling, Oct 13 2011

Status

approved