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A197512 Decimal expansion of least x>0 having cos(2x)=(cos pi*x/3)^2. 2
3, 0, 8, 1, 3, 7, 3, 5, 9, 9, 2, 8, 2, 3, 2, 6, 4, 6, 2, 3, 1, 7, 7, 0, 5, 6, 9, 9, 4, 5, 5, 4, 1, 1, 1, 9, 3, 9, 0, 5, 4, 8, 4, 3, 4, 9, 6, 7, 8, 8, 9, 4, 1, 4, 9, 5, 9, 3, 0, 9, 7, 0, 7, 6, 0, 3, 0, 2, 3, 7, 2, 0, 2, 2, 2, 4, 8, 1, 5, 5, 7, 2, 2, 9, 9, 5, 9, 9, 0, 2, 1, 0, 2, 1, 6, 1, 6, 9, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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=1..99.

EXAMPLE

x=3.0813735992823264623177056994554111...

MATHEMATICA

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

t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 3, 3.1}, WorkingPrecision -> 110]

RealDigits[t]   (* A197512 *)

Plot[{f[b*x], f[c*x]^2}, {x, 0, 4}]

CROSSREFS

Cf. A197476.

Sequence in context: A147600 A022895 A197416 * A232272 A186744 A200507

Adjacent sequences:  A197509 A197510 A197511 * A197513 A197514 A197515

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 16 2011

STATUS

approved

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Last modified April 9 20:55 EDT 2020. Contains 333363 sequences. (Running on oeis4.)