|
%I #7 Aug 23 2021 16:47:19
%S 1,6,9,0,7,7,6,4,7,3,9,8,0,1,5,1,4,9,9,9,5,2,9,5,3,6,7,6,7,2,6,2,7,8,
%T 1,0,7,4,2,1,3,4,0,7,6,9,6,9,6,5,3,7,1,7,0,5,6,2,1,0,6,7,7,0,2,8,1,3,
%U 5,0,2,5,7,5,8,9,1,6,8,6,1,8,9,9,4,5,5,6,8,0,9,5,5,1,1,9,4,7,8,0
%N Decimal expansion of the least x>0 satisfying sec(x)=6x.
%e x=0.169077647398015149995295367672627810742134076969653717056...
%t Plot[{1/x, Cos[x], 2 Cos[x], 3*Cos[x], 4 Cos[x]}, {x, 0, 2 Pi}]
%t t = x /. FindRoot[1/x == Cos[x], {x, .1, 5}, WorkingPrecision -> 100]
%t RealDigits[t] (* A133868 *)
%t t = x /. FindRoot[1/x == 2 Cos[x], {x, .5, .7}, WorkingPrecision -> 100]
%t RealDigits[t] (* A196603 *)
%t t = x /. FindRoot[1/x == 3 Cos[x], {x, .3, .4}, WorkingPrecision -> 100]
%t RealDigits[t] (* A196604 *)
%t t = x /. FindRoot[1/x == 4 Cos[x], {x, .1, .3}, WorkingPrecision -> 100]
%t RealDigits[t] (* A196605 *)
%t t = x /. FindRoot[1/x == 5 Cos[x], {x, .15, .23}, WorkingPrecision -> 100]
%t RealDigits[t] (* A196606 *)
%t t = x /. FindRoot[1/x == 6 Cos[x], {x, .1, .2}, WorkingPrecision -> 100]
%t RealDigits[t] (* A196607 *)
%o (PARI) solve(x=0,1,6*x*cos(x)-1) \\ _Charles R Greathouse IV_, Aug 23 2021
%K nonn,cons
%O 0,2
%A _Clark Kimberling_, Oct 04 2011
|
