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 A197521 #10 Feb 16 2025 05:39:20
%S A197521 3,5,2,1,3,3,7,8,2,9,5,7,1,7,1,5,6,9,8,6,9,1,9,8,8,5,6,4,4,5,4,9,1,7,
%T A197521 9,7,7,3,0,9,1,8,1,3,9,4,7,3,3,6,8,8,7,1,9,5,4,9,1,8,4,8,6,2,5,1,5,5,
%U A197521 9,0,6,0,9,6,1,0,2,5,9,8,8,8,9,7,4,9,7,5,6,9,0,0,3,9,4,9,7,1,5
%N A197521 Decimal expansion of least x>0 having cos(Pi*x/2)=(cos Pi*x/3)^2.
%C A197521 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 A197521 Conjecture: the constant here, 3.52133782..., is 3 plus the constant in A197383, the latter being the least t>0 satisfying sin(Pi*t/6)=(sin Pi*t/3)^2.
%C A197521 This number is irrational. I cannot prove it to be algebraic or transcendental. - _Charles R Greathouse IV_, Feb 16 2025
%e A197521 3.521337829571715698691988564454917977309181394...
%t A197521 b = Pi/2; c = Pi/3; f[x_] := Cos[x]
%t A197521 t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 3.5, 3.53}, WorkingPrecision -> 200]
%t A197521 RealDigits[t] (* A197521, appears to be 3+A197383 *)
%t A197521 Plot[{f[b*x], f[c*x]^2}, {x, 0, 4}]
%t A197521 RealDigits[ 6*ArcCos[ Root[ -1 - 4# + 4#^3 & , 2]]/Pi, 10, 99] // First (* _Jean-François Alcover_, Feb 19 2013 *)
%Y A197521 Cf. A197476.
%K A197521 nonn,cons
%O A197521 1,1
%A A197521 _Clark Kimberling_, Oct 16 2011