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A196623 Decimal expansion of the least x > 0 satisfying 1 = x*cos(x - Pi/5).

%I A196623 #9 Apr 10 2021 02:00:43
%S A196623 1,1,6,0,4,8,0,1,4,3,6,8,7,5,8,7,0,6,7,1,4,6,4,0,5,8,5,9,9,4,5,6,3,5,
%T A196623 8,8,9,1,7,5,4,9,9,3,4,7,3,5,9,5,0,5,2,4,5,3,1,5,9,7,3,0,6,6,0,7,9,7,
%U A196623 2,5,4,5,8,3,6,2,2,8,5,9,7,1,3,9,7,9,5,8,0,9,9,4,8,1,6,6,5,9,5,6
%N A196623 Decimal expansion of the least x > 0 satisfying 1 = x*cos(x - Pi/5).
%e A196623 x=1.1604801436875870671464058599456358891754993473595...
%t A196623 Plot[{1/x, Cos[x], Cos[x - Pi/2], Cos[x - Pi/3], Cos[x - Pi/4]}, {x,
%t A196623   0, 2 Pi}]
%t A196623 t = x /. FindRoot[1/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
%t A196623 RealDigits[t]  (* A133868 *)
%t A196623 t = x /. FindRoot[1/x == Cos[x - Pi/2], {x, .9, 1.3}, WorkingPrecision -> 100]
%t A196623 RealDigits[t]  (* A133866 *)
%t A196623 t = x /. FindRoot[1/x == Cos[x - Pi/3], {x, .9, 1.3}, WorkingPrecision -> 100]
%t A196623 RealDigits[t]  (* A196621 *)
%t A196623 t = x /. FindRoot[1/x == Cos[x - Pi/4], {x, .9, 1.2}, WorkingPrecision -> 100]
%t A196623 RealDigits[t]  (* A196622 *)
%t A196623 t = x /. FindRoot[1/x == Cos[x - Pi/5], {x, .9, 1.2}, WorkingPrecision -> 100]
%t A196623 RealDigits[t]  (* A196623 *)
%K A196623 nonn,cons
%O A196623 1,3
%A A196623 _Clark Kimberling_, Oct 05 2011