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 A197511 #15 Feb 16 2025 05:27:27
%S A197511 6,3,9,1,9,9,1,9,2,8,3,7,2,2,4,8,4,0,4,4,3,6,4,7,8,6,6,1,5,3,4,1,8,2,
%T A197511 8,8,3,3,4,3,2,2,1,1,8,1,9,9,8,6,4,1,7,3,7,5,6,3,9,8,9,0,4,6,6,8,9,0,
%U A197511 2,5,9,4,3,4,9,6,2,0,5,8,5,4,7,2,4,8,9,0,1,1,6,0,9,6,8,5,8,9,8
%N A197511 Decimal expansion of least x > 0 having cos(2*x) = cos(Pi*x/2)^2.
%C A197511 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 A197511 This number is irrational. I cannot prove it to be algebraic or transcendental. - _Charles R Greathouse IV_, Feb 16 2025
%e A197511 0.63919919283722484044364786615341828833...
%t A197511 b = 2; c = Pi/2; f[x_] := Cos[x]
%t A197511 t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .63, .64}, WorkingPrecision -> 110]
%t A197511 RealDigits[t] (* A197511 *)
%t A197511 Plot[{f[b*x], f[c*x]^2}, {x, 0, 1}]
%o A197511 (PARI) solve(x=.5,1, cos(2*x) - cos(Pi*x/2)^2) \\ _Charles R Greathouse IV_, Nov 26 2024
%Y A197511 Cf. A197476.
%K A197511 nonn,cons
%O A197511 0,1
%A A197511 _Clark Kimberling_, Oct 15 2011
%E A197511 a(98) corrected by _Sean A. Irvine_, Sep 08 2021