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Decimal expansion of the least x>0 satisfying 5*sec(x)=x.
5

%I #7 Aug 09 2021 14:04:21

%S 5,7,6,2,8,0,9,4,5,6,0,9,0,9,8,8,0,3,3,0,0,7,3,0,0,1,5,2,9,9,9,9,5,3,

%T 3,5,6,6,7,6,8,1,9,6,8,0,7,1,2,0,5,6,6,6,8,0,8,3,2,4,9,4,4,8,5,3,2,7,

%U 4,1,9,7,7,9,1,4,0,1,0,3,8,1,8,6,7,5,1,3,9,0,3,4,8,4,4,7,2,6,9,2,6,9,7,8,9

%N Decimal expansion of the least x>0 satisfying 5*sec(x)=x.

%e x=5.762809456090988033007300152999953356676...

%t Plot[{1/x, 2/x, 3/x, 4/x, Cos[x]}, {x, 0, 2 Pi}]

%t t = x /. FindRoot[1/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]

%t RealDigits[t] (* A133868 *)

%t t = x /. FindRoot[2/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196612 *)

%t t = x /. FindRoot[3/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196613 *)

%t t = x /. FindRoot[4/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196614 *)

%t t = x /. FindRoot[5/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196615 *)

%t t = x /. FindRoot[6/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196616 *)

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 05 2011