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A197519 Decimal expansion of least x>0 having cos(2*Pi*x)=(cos 2x)^2. 2
7, 5, 0, 7, 6, 2, 4, 9, 0, 2, 2, 7, 8, 8, 1, 2, 7, 5, 3, 4, 1, 9, 7, 3, 6, 3, 1, 4, 4, 3, 1, 3, 9, 0, 7, 8, 5, 6, 8, 2, 5, 7, 2, 2, 6, 5, 3, 6, 1, 7, 0, 5, 6, 2, 8, 1, 9, 2, 4, 9, 7, 2, 1, 3, 0, 1, 6, 8, 1, 6, 8, 8, 9, 7, 7, 7, 2, 5, 0, 4, 2, 1, 4, 2, 5, 2, 9, 2, 5, 2, 5, 6, 7, 6, 8, 3, 4, 1, 7 (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=0.7507624902278812753419736314431390785682572...

MATHEMATICA

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

t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .75, .76}, WorkingPrecision -> 200]

RealDigits[t]  (* A197519 *)

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

CROSSREFS

Cf. A197476.

Sequence in context: A096414 A144923 A184908 * A290374 A202350 A096435

Adjacent sequences:  A197516 A197517 A197518 * A197520 A197521 A197522

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 16 2011

STATUS

approved

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Last modified June 25 22:10 EDT 2019. Contains 324357 sequences. (Running on oeis4.)