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Decimal expansion of least x > 0 having sin(Pi*x/4) = sin(x/2)^2.
2

%I #14 Apr 10 2021 11:48:17

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

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

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

%N Decimal expansion of least x > 0 having sin(Pi*x/4) = 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.

%e x=2.53865633590794169787237029940757761479574...

%t b = Pi/4; c = 1/2; f[x_] := Sin[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 2.5, 2.6}, WorkingPrecision -> 200]

%t RealDigits[t](* A197393 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 2.8}]

%Y Cf. A197133.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 14 2011