A196821 - OEIS

%I #8 Feb 11 2025 13:55:26

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

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

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

%N Decimal expansion of the least x>0 satisfying 1/(1+x^2)=6*cos(x).

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e 1.5204494508338163631474588208905639631389853055832784...

%t Plot[{1/(1 + x^2), Cos[x], 2 Cos[x], 3 Cos[x], 4 Cos[x]}, {x, 0, 2}]

%t t = x /. FindRoot[1 == (1 + x^2) Cos[x], {x, 1, 1.5}, WorkingPrecision -> 100]

%t RealDigits[t]  (* A196816 *)

%t t = x /. FindRoot[1 == 2 (1 + x^2) Cos[x], {x, 1, 1.6},

%t    WorkingPrecision -> 100]

%t RealDigits[t]   (* A196817 *)

%t t = x /. FindRoot[1 == 3 (1 + x^2) Cos[x], {x, 1, 1.6},

%t    WorkingPrecision -> 100]

%t RealDigits[t]  (* A196818 *)

%t t = x /. FindRoot[1 == 4 (1 + x^2) Cos[x], {x, 1, 1.6},

%t    WorkingPrecision -> 100]

%t RealDigits[t]   (* A196819 *)

%t t = x /. FindRoot[1 == 5 (1 + x^2) Cos[x], {x, 1, 1.6},

%t    WorkingPrecision -> 100]

%t RealDigits[t]  (* A196820 *)

%t t = x /. FindRoot[1 == 6 (1 + x^2) Cos[x], {x, 1, 1.6},

%t    WorkingPrecision -> 100]

%t RealDigits[t]  (* A196821 *)

%Y Cf. A196914.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 06 2011