A197585 - OEIS

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A197585

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

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

(list; constant; graph; refs; listen; history; text; internal format)

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=0.4674563763333581675096373380169467059750...

MATHEMATICA

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

t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .46, .47}, WorkingPrecision -> 200]