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A196771 Decimal expansion of the least x > 0 satisfying 1 = x*sin(x - Pi/6).

%I A196771 #8 Apr 10 2021 08:05:31
%S A196771 1,3,5,4,2,8,7,2,1,4,1,5,7,7,2,1,4,1,7,8,3,0,6,3,7,1,6,1,6,3,7,5,3,0,
%T A196771 6,8,5,9,7,7,2,6,3,2,5,7,6,7,5,5,1,4,7,7,6,4,6,9,9,2,1,1,6,1,2,5,1,9,
%U A196771 2,2,3,4,1,6,4,3,7,6,0,3,8,8,1,9,0,8,5,8,3,0,1,8,6,4,0,3,5,0,2,1
%N A196771 Decimal expansion of the least x > 0 satisfying 1 = x*sin(x - Pi/6).
%e A196771 x=1.354287214157721417830637161637530685977263257675514...
%t A196771 Plot[{1/x, Sin[x], Sin[x - Pi/2], Sin[x - Pi/3], Sin[x - Pi/4]}, {x,
%t A196771   0, 2 Pi}]
%t A196771 t = x /. FindRoot[1/x == Sin[x], {x, 1, 1.2}, WorkingPrecision -> 100]
%t A196771 RealDigits[t]  (* A133866 *)
%t A196771 t = x /. FindRoot[1/x == Sin[x - Pi/2], {x, 1, 2}, WorkingPrecision -> 100]
%t A196771 RealDigits[t]     (* A196767 *)
%t A196771 t = x /. FindRoot[1/x == Sin[x - Pi/3], {x, 1, 2}, WorkingPrecision -> 100]
%t A196771 RealDigits[t]   (* A196768 *)
%t A196771 t = x /. FindRoot[1/x == Sin[x - Pi/4], {x, 1, 2}, WorkingPrecision -> 100]
%t A196771 RealDigits[t]    (* A196769 *)
%t A196771 t = x /. FindRoot[1/x == Sin[x - Pi/5], {x, 1, 2}, WorkingPrecision -> 100]
%t A196771 RealDigits[t]   (* A196770 *)
%t A196771 t = x /. FindRoot[1/x == Sin[x - Pi/6], {x, 1, 2}, WorkingPrecision -> 100]
%t A196771 RealDigits[t]    (* A196771 *)
%Y A196771 Cf. A196772.
%K A196771 nonn,cons
%O A196771 1,2
%A A196771 _Clark Kimberling_, Oct 06 2011