A197515 Decimal expansion of least x>0 having cos(Pi*x)=(cos x)^2.

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

Offset

1,2

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.

This number is irrational. I cannot prove it to be algebraic or transcendental. - Charles R Greathouse IV, Feb 16 2025

Links

Table of n, a(n) for n=1..99.

Example

1.501524980455762550683947262886278157...

Mathematica

b = Pi; c = 1; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.5, 1.502},
   WorkingPrecision -> 200]
RealDigits[t]  (* A197515 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 3}]

Crossrefs

Cf. A197476.

Sequence in context: A054672 A021670 A060081 * A326185 A293508 A083861

Adjacent sequences: A197512 A197513 A197514 * A197516 A197517 A197518

Keyword

nonn,cons,changed

Author

Clark Kimberling, Oct 16 2011

Status

approved