A196821 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=6*cos(x).

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, 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, 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

Offset: 1

Author

Clark Kimberling, Oct 06 2011

Keywords

• nonn
• cons

Examples

			1.5204494508338163631474588208905639631389853055832784...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A196914.

Programs

Mathematica

Plot[{1/(1 + x^2), Cos[x], 2 Cos[x], 3 Cos[x], 4 Cos[x]}, {x, 0, 2}]
t = x /. FindRoot[1 == (1 + x^2) Cos[x], {x, 1, 1.5}, WorkingPrecision -> 100]
RealDigits[t]  (* A196816 *)
t = x /. FindRoot[1 == 2 (1 + x^2) Cos[x], {x, 1, 1.6},
   WorkingPrecision -> 100]
RealDigits[t]   (* A196817 *)
t = x /. FindRoot[1 == 3 (1 + x^2) Cos[x], {x, 1, 1.6},
   WorkingPrecision -> 100]
RealDigits[t]  (* A196818 *)
t = x /. FindRoot[1 == 4 (1 + x^2) Cos[x], {x, 1, 1.6},
   WorkingPrecision -> 100]
RealDigits[t]   (* A196819 *)
t = x /. FindRoot[1 == 5 (1 + x^2) Cos[x], {x, 1, 1.6},
   WorkingPrecision -> 100]
RealDigits[t]  (* A196820 *)
t = x /. FindRoot[1 == 6 (1 + x^2) Cos[x], {x, 1, 1.6},
   WorkingPrecision -> 100]
RealDigits[t]  (* A196821 *)