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A196768 Decimal expansion of the least x > 0 satisfying 1 = x*sin(x - Pi/3).

%I A196768 #11 Aug 09 2021 14:07:57
%S A196768 1,6,8,3,3,0,5,5,8,6,7,0,8,8,9,6,1,4,5,4,3,7,3,6,1,7,5,8,9,9,4,8,5,5,
%T A196768 6,3,5,4,5,1,3,9,4,8,6,6,0,4,2,0,4,7,1,7,2,7,3,3,8,7,6,5,3,2,7,3,2,9,
%U A196768 2,9,6,6,5,6,0,6,5,7,1,5,8,2,3,9,6,4,2,9,2,5,4,4,5,0,5,6,5,1,6,6,6
%N A196768 Decimal expansion of the least x > 0 satisfying 1 = x*sin(x - Pi/3).
%e A196768 x=1.6833055867088961454373617589948556354513948660...
%t A196768 Plot[{1/x, Sin[x], Sin[x - Pi/2], Sin[x - Pi/3], Sin[x - Pi/4]}, {x,
%t A196768   0, 2 Pi}]
%t A196768 t = x /. FindRoot[1/x == Sin[x], {x, 1, 1.2}, WorkingPrecision -> 100]
%t A196768 RealDigits[t]  (* A133866 *)
%t A196768 t = x /. FindRoot[1/x == Sin[x - Pi/2], {x, 1, 2}, WorkingPrecision -> 100]
%t A196768 RealDigits[t]     (* A196767 *)
%t A196768 t = x /. FindRoot[1/x == Sin[x - Pi/3], {x, 1, 2}, WorkingPrecision -> 100]
%t A196768 RealDigits[t]   (* A196768 *)
%t A196768 t = x /. FindRoot[1/x == Sin[x - Pi/4], {x, 1, 2}, WorkingPrecision -> 100]
%t A196768 RealDigits[t]    (* A196769 *)
%t A196768 t = x /. FindRoot[1/x == Sin[x - Pi/5], {x, 1, 2}, WorkingPrecision -> 100]
%t A196768 RealDigits[t]   (* A196770 *)
%t A196768 t = x /. FindRoot[1/x == Sin[x - Pi/6], {x, 1, 2}, WorkingPrecision -> 100]
%t A196768 RealDigits[t]    (* A196771 *)
%Y A196768 Cf. A196772.
%K A196768 nonn,cons
%O A196768 1,2
%A A196768 _Clark Kimberling_, Oct 06 2011