A197512 - OEIS

%I #10 Feb 16 2025 05:30:44

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

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

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

%N Decimal expansion of least x > 0 having cos(2*x) = cos(Pi*x/3)^2.

%C 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.

%C This number is irrational. I cannot prove it to be algebraic or transcendental. - _Charles R Greathouse IV_, Feb 16 2025

%e 3.0813735992823264623177056994554111...

%t b = 2; c = Pi/3; f[x_] := Cos[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 3, 3.1}, WorkingPrecision -> 110]

%t RealDigits[t]   (* A197512 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 4}]

%Y Cf. A197476.

%K nonn,cons,changed

%O 1,1

%A _Clark Kimberling_, Oct 16 2011