A196402 Decimal expansion of the least positive number x satisfying e^(-x)=2*cos(x).

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

Offset

1,2

Links

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

Example

x=1.45367366646104161868434356812734006445958806...

Mathematica

Plot[{E^(-x), Cos[x], 2 Cos[x], 3 Cos[x], 4 Cos[x]}, {x, 0, Pi/2}]
t = x /. FindRoot[E^(-x) == Cos[x], {x, 1, 1.6}, WorkingPrecision -> 100];
RealDigits[t]  (* A196401 *)
t = x /. FindRoot[E^(-x) == 2 Cos[x], {x, 1, 1.6}, WorkingPrecision -> 100]; RealDigits[t]  (* A196402 *)
t = x /. FindRoot[E^(-x) == 3 Cos[x], {x, 1, 1.6}, WorkingPrecision -> 100]; RealDigits[t]  (* A196403 *)
t = x /. FindRoot[E^(-x) == 4 Cos[x], {x, 1, 1.6}, WorkingPrecision -> 100]; RealDigits[t]  (* A196404 *)
t = x /. FindRoot[E^(-x) == 5 Cos[x], {x, 1, 1.6}, WorkingPrecision -> 100]; RealDigits[t]  (* A196405 *)
t = x /. FindRoot[E^(-x) == 6 Cos[x], {x, 1, 1.6}, WorkingPrecision -> 100]; RealDigits[t]  (* A196406 *)

Crossrefs

Cf. A196401.

Sequence in context: A222627 A107793 A275275 * A268741 A263031 A004493

Adjacent sequences: A196399 A196400 A196401 * A196403 A196404 A196405

Keyword

nonn,cons

Author

Clark Kimberling, Oct 02 2011

Status

approved