A196602 Decimal expansion of the least x>0 satisfying 1=x*cos(3*x).

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

Offset

1,2

Links

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

Example

x=1.770823237218855899122052666084801060397231374306...

Mathematica

Plot[{1/x, Cos[x], Cos[2 x], Cos[3 x], Cos[4 x]}, {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[2 x], {x, 2, 3}, WorkingPrecision -> 100]
RealDigits[t]  (* A196608 *)
t = x /. FindRoot[1/x == Cos[3 x], {x, 1, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196602 *)
t = x /. FindRoot[1/x == Cos[4 x], {x, .9, 1.4}, WorkingPrecision -> 100]
RealDigits[t]  (* A196609 *)
t = x /. FindRoot[1/x == Cos[5 x], {x, .9, 1.2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196626 *)

Crossrefs

Sequence in context: A344382 A019725 A064890 * A200622 A357102 A258149

Adjacent sequences: A196599 A196600 A196601 * A196603 A196604 A196605

Keyword

nonn,cons

Author

Clark Kimberling, Oct 05 2011

Status

approved