login
A197492
Decimal expansion of least x > 0 having cos(x) = cos(Pi*x)^2.
2
8, 1, 1, 4, 9, 3, 3, 2, 1, 5, 0, 2, 4, 9, 6, 4, 3, 0, 2, 3, 2, 1, 6, 9, 5, 5, 4, 1, 1, 6, 6, 1, 3, 8, 1, 0, 6, 4, 0, 0, 1, 9, 8, 7, 8, 3, 2, 4, 0, 9, 3, 7, 5, 1, 0, 6, 4, 1, 4, 0, 8, 0, 6, 9, 3, 2, 9, 2, 5, 7, 1, 3, 8, 8, 9, 0, 4, 4, 0, 1, 6, 0, 0, 9, 7, 1, 1, 4, 4, 6, 6, 4, 0, 1, 1, 5, 2, 5, 8
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.
EXAMPLE
x=0.811493321502496430232169554116613810...
MATHEMATICA
b = 1; c = Pi; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .81, .82}, WorkingPrecision -> 110]
RealDigits[t] (* A197492 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/3}]
CROSSREFS
Cf. A197476.
Sequence in context: A154015 A300727 A246722 * A153621 A159822 A359540
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 15 2011
STATUS
approved