A197508 - OEIS

%I #18 Feb 16 2025 05:27:19

%S 5,0,6,2,9,7,8,9,9,2,3,4,0,5,9,8,2,6,7,5,0,0,1,1,5,6,2,7,8,3,6,9,7,0,

%T 3,2,5,2,8,6,5,8,1,6,3,9,5,8,2,8,9,4,7,4,1,9,1,4,3,2,4,7,4,1,1,1,0,7,

%U 6,9,2,2,7,8,9,7,5,3,6,7,6,3,4,2,8,4,5

%N Decimal expansion of least x > 0 having cos(2*x) = cos(3*Pi*x/2)^2.

%C 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 This number is irrational. I cannot prove it to be algebraic or transcendental. - _Charles R Greathouse IV_, Feb 16 2025

%e 0.50629789923405982675001156278369703252865816395828...

%t b = 2; c = 3 Pi/2; f[x_] := Cos[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .5, .51}, WorkingPrecision -> 110]

%t RealDigits[t] (* A197508 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/6}]

%Y Cf. A197476.

%K nonn,cons,changed

%O 0,1

%A _Clark Kimberling_, Oct 15 2011

%E a(87) onward corrected by _Sean A. Irvine_, Sep 08 2021