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 A197507 #14 Feb 16 2025 05:26:10
%S A197507 3,9,4,2,6,8,2,5,8,5,3,5,5,9,1,5,9,0,5,6,3,3,0,9,1,5,4,5,7,5,1,3,7,7,
%T A197507 4,0,9,5,5,0,1,7,2,9,4,0,8,4,1,8,3,4,3,9,7,9,6,1,7,3,6,5,7,1,0,4,6,0,
%U A197507 0,7,0,3,2,6,3,8,1,8,2,0,2,5,0,1,0,2,9,6,6,1,0,1,0,2,0,3,1,9,9
%N A197507 Decimal expansion of least x > 0 having cos(2*x) = cos(3*Pi*x)^2.
%C A197507 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 A197507 This number is irrational. I cannot prove it to be algebraic or transcendental. - _Charles R Greathouse IV_, Feb 16 2025
%e A197507 0.3942682585355915905633091545751377409550...
%t A197507 b = 2; c = 3 Pi; f[x_] := Cos[x]
%t A197507 t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .3, .4}, WorkingPrecision -> 110]
%t A197507 RealDigits[t] (* A197507 *)
%t A197507 Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/6}]
%Y A197507 Cf. A197476.
%K A197507 nonn,cons
%O A197507 0,1
%A A197507 _Clark Kimberling_, Oct 15 2011