A196826 Decimal expansion of the least x>0 satisfying 1/(1+x^2)=2*sin(x).

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

Offset

0,1

Links

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

Example

x=0.43420254999819638681352442196668401983962380...

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: A286953 A170987 A239735 * A215597 A266110 A204819

Adjacent sequences: A196823 A196824 A196825 * A196827 A196828 A196829

Keyword

nonn,cons

Author

Clark Kimberling, Oct 07 2011

Status

approved