A196767 Decimal expansion of the least x > 0 satisfying 1 = x*sin(x - Pi/2), or, equivalently, -1 = x*cos(x).

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

Offset

1,1

Links

Table of n, a(n) for n=1..101.

Example

x=2.073932809091214901167776297799360067946219531...

Mathematica

Plot[{1/x, Sin[x], Sin[x - Pi/2], Sin[x - Pi/3], Sin[x - Pi/4]}, {x,
  0, 2 Pi}]
t = x /. FindRoot[1/x == Sin[x], {x, 1, 1.2}, WorkingPrecision -> 100]
RealDigits[t]  (* A133866 *)
t = x /. FindRoot[1/x == Sin[x - Pi/2], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]     (* A196767 *)
t = x /. FindRoot[1/x == Sin[x - Pi/3], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]   (* A196768 *)
t = x /. FindRoot[1/x == Sin[x - Pi/4], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]    (* A196769 *)
t = x /. FindRoot[1/x == Sin[x - Pi/5], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]   (* A196770 *)
t = x /. FindRoot[1/x == Sin[x - Pi/6], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]    (* A196771 *)

Crossrefs

Cf. A196772.

Sequence in context: A300702 A353273 A105394 * A307216 A011343 A326731

Adjacent sequences: A196764 A196765 A196766 * A196768 A196769 A196770

Keyword

nonn,cons

Author

Clark Kimberling, Oct 06 2011

Status

approved