A197513 - OEIS

%I #10 Feb 16 2025 05:30:41

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

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

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

%N Decimal expansion of least x > 0 having cos(2*x) = cos(Pi*x/4)^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 2.4052337038770365360381128025228272460264...

%t b = 2; c = Pi/4; f[x_] := Cos[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 2.4, 2.41}, WorkingPrecision -> 110]

%t RealDigits[t]  (* A197513 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 3}]

%Y Cf. A197476.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 16 2011