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A197506 Decimal expansion of least x>0 having cos(x)=(cos 2*pi*x/3)^2. 2
1, 1, 0, 1, 9, 6, 9, 5, 6, 5, 5, 4, 4, 0, 6, 8, 6, 6, 9, 4, 9, 6, 9, 1, 2, 8, 3, 5, 8, 8, 6, 2, 6, 7, 2, 2, 1, 9, 9, 8, 4, 4, 3, 3, 3, 3, 6, 0, 6, 2, 2, 9, 1, 2, 0, 7, 6, 6, 2, 5, 7, 2, 2, 0, 0, 8, 3, 9, 8, 9, 8, 7, 2, 1, 8, 9, 7, 9, 5, 0, 2, 9, 0, 3, 6, 9, 0, 5, 9, 2, 5, 5, 5, 0, 2, 6, 5, 2, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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=1.101969565544068669496912835886267221998...

MATHEMATICA

b = 1; c = 2 Pi/3; f[x_] := Cos[x]

t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.1, 1.2}, WorkingPrecision -> 110]

RealDigits[t] (* A197506 *)

Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/2}]

CROSSREFS

Cf. A197476.

Sequence in context: A083281 A019711 A010545 * A225452 A230161 A019790

Adjacent sequences:  A197503 A197504 A197505 * A197507 A197508 A197509

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 15 2011

STATUS

approved

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Last modified June 24 09:37 EDT 2019. Contains 324323 sequences. (Running on oeis4.)