|
%I #8 Apr 10 2021 08:05:16
%S 1,0,3,0,9,1,5,3,4,8,5,3,5,1,1,3,4,1,1,8,6,4,3,8,4,0,1,8,3,5,3,4,3,5,
%T 6,6,2,0,9,0,6,1,6,9,3,2,9,4,0,1,9,2,2,2,3,3,8,0,6,0,2,3,3,5,7,8,9,8,
%U 4,3,2,8,3,3,5,2,1,8,0,1,6,0,6,0,2,6,9,9,4,1,7,0,3,6,1,6,7,7,6,9
%N Decimal expansion of the least x > 0 satisfying 1 = x*cos(x - Pi/4).
%e x=1.03091534853511341186438401835343566209061693...
%t Plot[{1/x, Cos[x], Cos[x - Pi/2], Cos[x - Pi/3], Cos[x - Pi/4]}, {x,
%t 0, 2 Pi}]
%t t = x /. FindRoot[1/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
%t RealDigits[t] (* A133868 *)
%t t = x /. FindRoot[1/x == Cos[x - Pi/2], {x, .9, 1.3}, WorkingPrecision -> 100]
%t RealDigits[t] (* A133866 *)
%t t = x /. FindRoot[1/x == Cos[x - Pi/3], {x, .9, 1.3}, WorkingPrecision -> 100]
%t RealDigits[t] (* A196621 *)
%t t = x /. FindRoot[1/x == Cos[x - Pi/4], {x, .9, 1.2}, WorkingPrecision -> 100]
%t RealDigits[t] (* A196622 *)
%t t = x /. FindRoot[1/x == Cos[x - Pi/5], {x, .9, 1.2}, WorkingPrecision -> 100]
%t RealDigits[t] (* A196623 *)
%K nonn,cons
%O 1,3
%A _Clark Kimberling_, Oct 05 2011
|
