A197571 Decimal expansion of least x > 0 having cos(x) = cos(3*Pi*x)^2.

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

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=0.275155855079987513770985820902137972...

Mathematica

b = 1; c = 3*Pi; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .27, .28}, WorkingPrecision -> 200]
RealDigits[t] (* A197571 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, .5}]

Crossrefs

Cf. A197133.

Sequence in context: A244678 A201319 A110945 * A178422 A296564 A266262

Adjacent sequences: A197568 A197569 A197570 * A197572 A197573 A197574

Keyword

nonn,cons

Author

Clark Kimberling, Oct 16 2011

Status

approved