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A196770 Decimal expansion of the least x > 0 satisfying 1 = x*sin(x - Pi/5).

%I A196770 #8 Apr 10 2021 08:05:23
%S A196770 1,4,1,3,9,2,2,5,4,0,9,0,9,2,9,6,7,4,0,4,2,4,4,5,3,3,3,3,0,3,6,0,3,3,
%T A196770 1,1,3,0,4,0,9,0,1,9,1,5,7,1,0,0,0,8,3,1,5,0,5,5,0,3,1,6,0,0,5,8,0,6,
%U A196770 3,7,8,3,6,7,5,4,0,2,7,3,0,1,2,4,9,0,2,5,7,2,8,1,9,1,2,2,6,1,8,7
%N A196770 Decimal expansion of the least x > 0 satisfying 1 = x*sin(x - Pi/5).
%e A196770 x=1.41392254090929674042445333303603311304090191571000...
%t A196770 Plot[{1/x, Sin[x], Sin[x - Pi/2], Sin[x - Pi/3], Sin[x - Pi/4]}, {x,
%t A196770   0, 2 Pi}]
%t A196770 t = x /. FindRoot[1/x == Sin[x], {x, 1, 1.2}, WorkingPrecision -> 100]
%t A196770 RealDigits[t]  (* A133866 *)
%t A196770 t = x /. FindRoot[1/x == Sin[x - Pi/2], {x, 1, 2}, WorkingPrecision -> 100]
%t A196770 RealDigits[t]     (* A196767 *)
%t A196770 t = x /. FindRoot[1/x == Sin[x - Pi/3], {x, 1, 2}, WorkingPrecision -> 100]
%t A196770 RealDigits[t]   (* A196768 *)
%t A196770 t = x /. FindRoot[1/x == Sin[x - Pi/4], {x, 1, 2}, WorkingPrecision -> 100]
%t A196770 RealDigits[t]    (* A196769 *)
%t A196770 t = x /. FindRoot[1/x == Sin[x - Pi/5], {x, 1, 2}, WorkingPrecision -> 100]
%t A196770 RealDigits[t]   (* A196770 *)
%t A196770 t = x /. FindRoot[1/x == Sin[x - Pi/6], {x, 1, 2}, WorkingPrecision -> 100]
%t A196770 RealDigits[t]    (* A196771 *)
%Y A196770 Cf. A196772.
%K A196770 nonn,cons
%O A196770 1,2
%A A196770 _Clark Kimberling_, Oct 06 2011