OFFSET
0,1
COMMENTS
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.
EXAMPLE
x=0.88736048447785163686131425680836901251306...
MATHEMATICA
b = Pi/4; c = Pi/3; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 0.8, 1}, WorkingPrecision -> 200]
RealDigits[t] (* A197381 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 2}]
(* or *)
RealDigits[12*ArcTan[Sqrt[Root[9 - 217*#1 + 1085*#1^2 - 1501*#1^3 + 1019*#1^4 - 267*#1^5 - #1^6 + #1^7 & , 2]]]/Pi, 10, 120][[1]] (* Vaclav Kotesovec, Nov 14 2015 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 14 2011
STATUS
approved