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

%I #13 Jan 12 2025 14:15:40

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

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

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

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

%e x=0.4699114005769069609291973665527752008160...

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

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .45, .47}, WorkingPrecision -> 200]

%t RealDigits[t] (* A197575 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.6}]

%Y Cf. A197133.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 16 2011

%E Name corrected by _Sean A. Irvine_, Jan 12 2025