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A197510 Decimal expansion of least x > 0 having cos(2*x) = cos(Pi*x)^2. 2
6, 6, 3, 4, 9, 0, 0, 4, 6, 0, 5, 6, 6, 3, 7, 3, 2, 0, 7, 8, 9, 8, 3, 6, 1, 6, 6, 9, 1, 5, 1, 9, 0, 2, 1, 3, 3, 2, 1, 5, 0, 3, 2, 7, 9, 6, 4, 5, 8, 6, 8, 0, 6, 0, 0, 9, 3, 9, 2, 7, 8, 8, 8, 1, 7, 1, 0, 9, 3, 2, 8, 4, 7, 9, 2, 1, 9, 4, 6, 9, 2, 3, 6, 6, 4, 7, 1, 7, 6, 8, 4, 0, 2, 6, 3, 8, 9, 5, 1 (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
EXAMPLE
x=0.66349004605663732078983616691519021...
MATHEMATICA
b = 2; c = Pi; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .6, .7}, WorkingPrecision -> 110]
RealDigits[t] (* A197510 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 1}]
CROSSREFS
Cf. A197476.
Sequence in context: A112112 A193085 A338004 * A360958 A110632 A202068
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 15 2011
STATUS
approved

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)