A197575 Decimal expansion of least x > 0 having cos(x) = cos(Pi*x/2)^2.

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

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

Table of n, a(n) for n=0..98.

Example

x=0.4699114005769069609291973665527752008160...

Mathematica

b = 1; c = Pi/2; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .45, .47}, WorkingPrecision -> 200]
RealDigits[t] (* A197575 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.6}]

Crossrefs

Cf. A197133.

Sequence in context: A236536 A084335 A277893 * A201660 A341577 A094115

Adjacent sequences: A197572 A197573 A197574 * A197576 A197577 A197578

Keyword

nonn,cons

Author

Clark Kimberling, Oct 16 2011

Status

approved