%I #17 Feb 14 2025 17:18:03

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

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

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

%N Decimal expansion of least x > 0 having sin(x) = sin(4*Pi*x)^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 0.212071071918104282044351175694283522568520305091...

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

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .21, .22}, WorkingPrecision -> 200]

%t RealDigits[t] (* A197522 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, .5}]

%Y Cf. A197133.

%K nonn,cons,changed

%O 0,1

%A _Clark Kimberling_, Oct 16 2011

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