A197477 Decimal expansion of least x>0 having cos(x)=(cos 3x)^2.

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

Offset: 0

Author

Clark Kimberling, Oct 15 2011

Keywords

• nonn
• cons

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.

Examples

			0.8418355356143638074857326765621643076...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A197476.

Programs

Mathematica

b = 1; c = 3; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .8, .9}, WorkingPrecision -> 200]
RealDigits[t] (* A197477 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/2}]
RealDigits[ ArcCos[ Root[ 1 - 8# - 8#^2 + 16#^3 + 16#^4 &, 2]], 10, 99] // First (* Jean-François Alcover, Feb 19 2013 *)