A196828 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=4*sin(x).

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

Offset

0,1

Links

Table of n, a(n) for n=0..99.

Example

x=0.238777659445904852564729030954613747638153989...

Mathematica

Plot[{1/(1 + x^2), Sin[x], 2 Sin[x], 3 Sin[x], 4 Sin[x]}, {x, 0, 2}]
t = x /. FindRoot[1 == (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A196825 *)
t = x /. FindRoot[1 == 2 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A196826 *)
t = x /. FindRoot[1 == 3 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A196827 *)
t = x /. FindRoot[1 == 4 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A196828 *)
t = x /. FindRoot[1 == 5 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A196829 *)
t = x /. FindRoot[1 == 6 (1 + x^2) Sin[x], {x, 0, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A196830 *)

Crossrefs

Cf. A196832.

Sequence in context: A265366 A265365 A183141 * A171046 A250116 A318949

Adjacent sequences: A196825 A196826 A196827 * A196829 A196830 A196831

Keyword

nonn,cons

Author

Clark Kimberling, Oct 07 2011

Status

approved