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A196621 Decimal expansion of the least x > 0 satisfying 1 = x*cos(x - Pi/3).

%I A196621 #8 Apr 10 2021 08:05:09
%S A196621 1,0,0,1,0,6,5,0,4,8,3,2,5,5,4,6,0,2,8,4,7,1,3,0,7,2,9,0,3,0,5,4,0,3,
%T A196621 4,8,4,5,6,7,7,6,1,4,1,8,7,4,9,0,5,3,6,4,4,3,8,3,1,9,1,4,0,8,4,2,3,9,
%U A196621 0,6,9,5,4,3,0,4,9,0,1,7,8,3,6,4,0,6,5,0,7,9,7,8,4,4,4,4,6,2,9,5
%N A196621 Decimal expansion of the least x > 0 satisfying 1 = x*cos(x - Pi/3).
%e A196621 x=1.0010650483255460284713072903054034845677614187490536443...
%t A196621 Plot[{1/x, Cos[x], Cos[x - Pi/2], Cos[x - Pi/3], Cos[x - Pi/4]}, {x,
%t A196621   0, 2 Pi}]
%t A196621 t = x /. FindRoot[1/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
%t A196621 RealDigits[t]  (* A133868 *)
%t A196621 t = x /. FindRoot[1/x == Cos[x - Pi/2], {x, .9, 1.3}, WorkingPrecision -> 100]
%t A196621 RealDigits[t]  (* A133866 *)
%t A196621 t = x /. FindRoot[1/x == Cos[x - Pi/3], {x, .9, 1.3}, WorkingPrecision -> 100]
%t A196621 RealDigits[t]  (* A196621 *)
%t A196621 t = x /. FindRoot[1/x == Cos[x - Pi/4], {x, .9, 1.2}, WorkingPrecision -> 100]
%t A196621 RealDigits[t]  (* A196622 *)
%t A196621 t = x /. FindRoot[1/x == Cos[x - Pi/5], {x, .9, 1.2}, WorkingPrecision -> 100]
%t A196621 RealDigits[t]  (* A196623 *)
%Y A196621 Cf. A196625.
%K A196621 nonn,cons
%O A196621 1,6
%A A196621 _Clark Kimberling_, Oct 05 2011