A197376 - OEIS

%I #15 Feb 14 2025 17:34:36

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

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

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

%N Decimal expansion of least x>0 having sin(x)=(sin (x/2))^2.

%C The Mathematica program includes a graph.  See A197133 for a guide to least x>0 satisfying sin(b*x)=(sin(c*x))^2 for selected b and c.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%F Equals 2*A105199. - _R. J. Mathar_, Aug 27 2024

%e 2.2142974355881810060341309203570740...

%t b = 1; c = 1/2; f[x_] := Sin[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 2, 2.5}, WorkingPrecision -> 200]

%t RealDigits[t] (*  *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 2.5}]

%t RealDigits[ 2*ArcCos[ 1/Sqrt[5] ], 10, 99] // First (* _Jean-François Alcover_, Feb 19 2013 *)

%Y Cf. A197133.

%K nonn,cons,changed

%O 1,1

%A _Clark Kimberling_, Oct 14 2011