A197578 Decimal expansion of least x > 0 having cos(Pi*x) = cos(3*x)^2.

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

Offset

0,1

Comments

The Mathematica program includes a graph. See A197476 for a guide for the least x > 0 satisfying cos(b*x) = cos(c*x)^2 for selected b and c.

Links

Table of n, a(n) for n=0..98.

Example

x=0.51355833431133750362682607984081144812946470068...

Mathematica

b = Pi; c = 3; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .51, .52}, WorkingPrecision -> 200]
RealDigits[t] (* A197578 *)
Plot[{f[b*x], f[c*x]^2}, {x, .4, .6}]

Crossrefs

Cf. A197133.

Sequence in context: A153457 A057778 A071545 * A115370 A327968 A213815

Adjacent sequences: A197575 A197576 A197577 * A197579 A197580 A197581

Keyword

nonn,cons

Author

Clark Kimberling, Oct 16 2011

Status

approved