This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A197509 #13 Feb 16 2025 05:27:22
%S A197509 4,0,5,7,4,6,6,6,0,7,5,1,2,4,8,2,1,5,1,1,6,0,8,4,7,7,7,0,5,8,3,0,6,9,
%T A197509 0,5,3,2,0,0,0,9,9,3,9,1,6,2,0,4,6,8,7,5,5,3,2,0,7,0,4,0,3,4,6,6,4,6,
%U A197509 2,8,5,6,9,4,4,5,2,2,0,0,8,0,0,4,8,5,5,7,2,3,3,2,0,0,5,7,6,2,9
%N A197509 Decimal expansion of least x > 0 having cos(2*x) = cos(2*Pi*x)^2.
%C A197509 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 A197509 This number is irrational. I cannot prove it to be algebraic or transcendental. - _Charles R Greathouse IV_, Feb 16 2025
%e A197509 0.40574666075124821511608477705830690...
%t A197509 b = 2; c = 2 Pi; f[x_] := Cos[x]
%t A197509 t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .4, .5}, WorkingPrecision -> 110]
%t A197509 RealDigits[t] (* A197509 *)
%t A197509 Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/6}]
%Y A197509 Cf. A197476.
%K A197509 nonn,cons
%O A197509 0,1
%A A197509 _Clark Kimberling_, Oct 15 2011