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 A197506 #15 Feb 16 2025 05:26:16
%S A197506 1,1,0,1,9,6,9,5,6,5,5,4,4,0,6,8,6,6,9,4,9,6,9,1,2,8,3,5,8,8,6,2,6,7,
%T A197506 2,2,1,9,9,8,4,4,3,3,3,3,6,0,6,2,2,9,1,2,0,7,6,6,2,5,7,2,2,0,0,8,3,9,
%U A197506 8,9,8,7,2,1,8,9,7,9,5,0,2,9,0,3,6,9,0,5,9,2,5,5,5,0,2,6,5,2,0
%N A197506 Decimal expansion of least x > 0 having cos(x) = cos(2*Pi*x/3)^2.
%C A197506 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 A197506 This number is irrational. I cannot prove it to be algebraic or transcendental. - _Charles R Greathouse IV_, Feb 16 2025
%e A197506 1.101969565544068669496912835886267221998...
%t A197506 b = 1; c = 2 Pi/3; f[x_] := Cos[x]
%t A197506 t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.1, 1.2}, WorkingPrecision -> 110]
%t A197506 RealDigits[t] (* A197506 *)
%t A197506 Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/2}]
%Y A197506 Cf. A197476.
%K A197506 nonn,cons
%O A197506 1,5
%A A197506 _Clark Kimberling_, Oct 15 2011
%E A197506 Offset corrected by _Georg Fischer_, Jul 28 2021