A196825 Decimal expansion of the least x > 0 satisfying 1/(1 + x^2) = sin(x).

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

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Example

0.7194212963274103157169229700373320490851010...

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 *)

Prog

(PARI) a=1; c=1; solve(x=0.5, 1, a*x^2 + c - 1/sin(x)) // G. C. Greubel, Aug 21 2018

Crossrefs

Cf. A196832.

Sequence in context: A200288 A117493 A177515 * A021143 A153870 A176437

Adjacent sequences: A196822 A196823 A196824 * A196826 A196827 A196828

Keyword

nonn,cons

Author

Clark Kimberling, Oct 07 2011

Status

approved