A196623 Decimal expansion of the least x > 0 satisfying 1 = x*cos(x - Pi/5).

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

Offset

1,3

Links

Table of n, a(n) for n=1..100.

Example

x=1.1604801436875870671464058599456358891754993473595...

Mathematica

Plot[{1/x, Cos[x], Cos[x - Pi/2], Cos[x - Pi/3], Cos[x - Pi/4]}, {x,
  0, 2 Pi}]
t = x /. FindRoot[1/x == Cos[x], {x, 4, 7}, WorkingPrecision -> 100]
RealDigits[t]  (* A133868 *)
t = x /. FindRoot[1/x == Cos[x - Pi/2], {x, .9, 1.3}, WorkingPrecision -> 100]
RealDigits[t]  (* A133866 *)
t = x /. FindRoot[1/x == Cos[x - Pi/3], {x, .9, 1.3}, WorkingPrecision -> 100]
RealDigits[t]  (* A196621 *)
t = x /. FindRoot[1/x == Cos[x - Pi/4], {x, .9, 1.2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196622 *)
t = x /. FindRoot[1/x == Cos[x - Pi/5], {x, .9, 1.2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196623 *)

Crossrefs

Sequence in context: A100120 A132709 A197148 * A265275 A113024 A112280

Adjacent sequences: A196620 A196621 A196622 * A196624 A196625 A196626

Keyword

nonn,cons

Author

Clark Kimberling, Oct 05 2011

Status

approved