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A197507 Decimal expansion of least x>0 having cos(2x)=(cos 3*pi*x )^2. 2
3, 9, 4, 2, 6, 8, 2, 5, 8, 5, 3, 5, 5, 9, 1, 5, 9, 0, 5, 6, 3, 3, 0, 9, 1, 5, 4, 5, 7, 5, 1, 3, 7, 7, 4, 0, 9, 5, 5, 0, 1, 7, 2, 9, 4, 0, 8, 4, 1, 8, 3, 4, 3, 9, 7, 9, 6, 1, 7, 3, 6, 5, 7, 1, 0, 4, 6, 0, 0, 7, 0, 3, 2, 6, 3, 8, 1, 8, 2, 0, 2, 5, 0, 1, 0, 2, 9, 6, 6, 1, 0, 1, 0, 2, 0, 3, 1, 9, 9 (list; constant; graph; refs; listen; history; text; internal format)
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=0.3942682585355915905633091545751377409550...

MATHEMATICA

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

t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .3, .4}, WorkingPrecision -> 110]

RealDigits[t] (* A197507 *)

Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/6}]

CROSSREFS

Cf. A197476.

Sequence in context: A200012 A130701 A202021 * A264992 A050000 A154368

Adjacent sequences:  A197504 A197505 A197506 * A197508 A197509 A197510

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 15 2011

STATUS

approved

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Last modified July 23 22:38 EDT 2019. Contains 325278 sequences. (Running on oeis4.)