_Clark Kimberling (ck6(AT)evansville.edu), _, Oct 16 2011

proposed

approved

editing

proposed

allocated for Clark KimberlingDecimal expansion of least x>0 having cos(2*Pi*x)=(cos x)^2.

8, 2, 5, 9, 7, 9, 1, 5, 6, 8, 1, 1, 2, 5, 0, 3, 9, 4, 8, 8, 2, 3, 3, 9, 1, 4, 2, 8, 6, 7, 2, 2, 3, 6, 0, 1, 9, 0, 6, 3, 2, 7, 9, 1, 9, 7, 7, 9, 5, 3, 9, 2, 0, 1, 5, 0, 5, 3, 4, 0, 9, 4, 4, 3, 5, 6, 2, 7, 1, 1, 5, 6, 9, 7, 8, 3, 4, 4, 7, 2, 9, 3, 8, 5, 0, 2, 6, 2, 0, 7, 0, 6, 1, 7, 2, 0, 5, 5, 6

0,1

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.

x=0.825979156811250394882339142867223601906327919779...

b = 2 Pi; c = 1; f[x_] := Cos[x]

t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .8, .9}, WorkingPrecision -> 200]

RealDigits[t] (* A197518 *)

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

Cf. A197476.

allocated

nonn,cons

Clark Kimberling (ck6(AT)evansville.edu), Oct 16 2011

approved

editing

allocated for Clark Kimberling

allocated

approved