A197574 Decimal expansion of least x > 0 having cos(x) = cos(Pi*x)^2.

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

Offset

0,3

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=0.104875999711743873968413894326481617617881...

Mathematica

b = 1; c = Pi; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .1, .11}, WorkingPrecision -> 200]
RealDigits[t] (* A197574 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.2}]

Crossrefs

Cf. A197133.

Sequence in context: A309818 A201658 A146501 * A337606 A019924 A021209

Adjacent sequences: A197571 A197572 A197573 * A197575 A197576 A197577

Keyword

nonn,cons

Author

Clark Kimberling, Oct 16 2011

Status

approved