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A197520 Decimal expansion of least x>0 having cos(2*Pi*x)=(cos 3x)^2. 2
9, 0, 6, 3, 6, 2, 2, 3, 6, 5, 3, 8, 7, 2, 1, 4, 1, 7, 5, 1, 9, 6, 9, 1, 9, 2, 2, 7, 5, 8, 8, 4, 6, 9, 1, 0, 3, 1, 2, 0, 8, 8, 7, 1, 0, 3, 0, 1, 9, 2, 0, 1, 8, 0, 4, 1, 4, 4, 0, 8, 9, 3, 8, 8, 7, 3, 7, 2, 3, 9, 2, 8, 6, 2, 0, 8, 5, 9, 6, 8, 1, 5, 6, 0, 8, 2, 0, 2, 8, 8, 5, 2, 4, 6, 7, 6, 1, 3, 4 (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=0.9063622365387214175196919227588469103120887...

MATHEMATICA

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

t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .9, .91}, WorkingPrecision -> 200]

RealDigits[t]   (* A197520 *)

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

CROSSREFS

Cf. A197476.

Sequence in context: A188738 A199789 A019874 * A068467 A131223 A225464

Adjacent sequences:  A197517 A197518 A197519 * A197521 A197522 A197523

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 16 2011

STATUS

approved

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Last modified February 19 22:38 EST 2019. Contains 320328 sequences. (Running on oeis4.)